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**RF & Microwave Fundamentals**

Jan 2006 Anritsu Korea

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**Basic Fudamentals • Definition of Terms • What Does RF Mean?**

• Basic Concepts • Transmission Lines • Coaxial Cable • Waveguide • Transmission Line Theory • Transmission measurements and error analysis • Return Loss measurements and error analysis • Advanced Measurement Techniques (air lines) • S Parameters & VNA measurement fundamentals • Common Microwave Devices and measurements • Synthesizer related RF Concepts References: The ARRL Handbook for Radio Amateurs, Published by American Radio Relay League. 1997 Practical Microwaves by Thomas S. Laverghetta RF Circuit Design by Joseph J. Carr The Essential Guide to RF and Wireless by Carl J. Weisman 1990 notes and Basic RF notes from JK

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**Electromagnetic Spectrum**

RF Radio Frequency. A general term used to describe the frequency range from 3 kHz to 3.0 GHz (Gigahertz ) Microwave. The frequency range 3GHz to 30.0 GHz. Above 1 GHz, lumped circuit elements are replaced by distributed circuit elements. Millimeter wave. The frequency range 30 GHz to 300 GHz. The corresponding wavelength is less than a centimeter. Radio Frequency. A general term used to describe the entire range of alternating voltage or current, ranging from 3 kHz to 300 GHz. The RF frequency range covers the following sub-sets, microwave, and millimeter wave. We shall use the term RF to apply to all the aforementioned. Microwave. A subset of RF, 1GHz to 300 GHz. Above 1 GHz, circuit elements are replaced by lumped-constant circuit elements. Millimeter wave. A subset of Microwaves, 20 GHz to 300 GHz. The corresponding wavelength is less than a centimeter. Electromagnetic Spectrum. This terms is sometimes used to describe an even broader frequency range than RF. It includes the entire range of wavelengths or frequencies of electromagnetic radiation ranging from gamma rays to the longest radio waves and including visible light. (Webster, 1995). This term is too broad for our purposes so we shall not use it.

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**Range of RF Frequencies**

Medium Frequency (300 KHz - 3 MHz) High Frequency (HF) ( MHz) Very High Frequency (VHF) ( MHz) Ultra High Frequency (UHF) ( MHz)

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**Some Terms You Will Hear**

dB dBm Impedance Return Loss (RL) Insertion Loss (Cable Loss) VSWR DTF Watts dB - a mathematical conversion, utilizing logarithms of ratio, which is used as a unit of measure for RF signals. It is primarily used as a measure of the (power) gain and insertion loss of RF components and/or systems. dBm - same as dB, but referenced to 1.0 milliwatt Impedance - A measure of an RF component’s input and output “size,” in terms of electrical resistance (impedance) expressed in ohms. In RF systems, the standard or characteristic impedance used by all components is referred to as 50 ohms. Return Loss- A measure of match between RF components, expressed in decibels (dBs).The better the match, the less energy reflected, the better (higher) the return loss. Insertion Loss - A measure of how much smaller the output signal of a passive device is with respect to the input signal, that is, cable loss. Insertion loss is measured in decibels (dBs). VSWR - A measure of match between two RF components, expressed as a ratio of X:1 (X1). The lower the X, the better the match. DTF - Distance-to-Fault. A measure pinpointing the location and reflection amplitude of a transmission line and its components, for example, connectors, etc. Watts - A unit of measure of any kind of power, that is, RF, heat, etc.

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**Linear vs Log Some things are very, very large.**

Some things are very, very small. It is difficult to express comparison of sizes in common units of measure with a linear scale. One would not usually express a flea’s dimensions in miles, for example. Consider a 1 µV signal delivered to a 72 ohm input of a radio receiver. The power received by the radio would be: P = E2/ R P = ( )2/ 72 = Watts or P = 1.39 × Watts Let say that the RF power transmitted might be 1,390,000 Watts or 1.39 × 106 Watts The signal arriving at the receiver is what fraction of the transmitted power? Ratio = (1.39 × )/ (1.39 × 106 ) = 1 × 10-20 Such numbers are hard to visualize, and keeping track of the zeros is almost impossible. An order of magnitude involves a factor of 10. It is much easier to make such calculations in terms of factors of 10. To simplify matters further, a factor of 10 has been defined as a bel. Hence we can say that the received signal (power) is 20 bels less than the transmitted power, or the transmitted power is 20 bels greater than the received power.

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**Bel A bel is defined as the logarithm of a power ratio. Po bel = log**

Pi The bel is named after a Scottish-American scientist Alexander Graham Bell ( ), who invented the telephone and did much pioneer work with sound and the way our ears respond to sound. Po bel = log Pi Where Pi the reference power (or the input power) Po is the power you are comparing to the reference level (or the output power) Let us solve for the number of bels from our example. Let Po = 1.39 × Watts Pi = 1.39 × 106 Watts bel = log (Po/ Pi) = log{(1.39 × )/ (1.39 × 106 )} = log (1 × 10-20) = - 20 bels

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Decibel (dB) Decibel (dB) is a logarithmic unit of relative power measurement that expresses the ratio of two power levels. Po dB = 10 log Pi The decibel is one-tenth of a bel, and is abbreviated dB. If we have an amplifier with its input power of 2 watts and its output power of 50 watts. What is the gain of the amplifier in dB? dB = 10 log (50/2) = 10 log (25) = dB Therefore, the amplifier has a gain of nearly 14 dB.

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**dBm dBm is the decibel value of a signal compared to 1 m w.**

The dBm unit refers to decibels relative to 1 mW dissipated in a 50 ohm resistive impedance ( defined as the 0-dBm reference level) and is calculated from dBm = 10 log ( PW/ 0.001) or = 10 log ( PMW) Example: How much is the the power of 5.6 × W in dBm? dBm = 10 log {(5.6 × 10-10)/ 0.001} = 10 log (5.6 × 10-7) = dBm

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**3 dB rule +3 dB means double the power (multiply by 2)**

- 3 dB means halve the power (divide by 2) The total power can be calculated by inspection. Each time you double the power, there is 3 dB increase. If you double the power again, there would be a 6 dB increase. Double the power a third time, there would be a 9 dB increase. Double the power a fourth time, there would be a 12 dB increase. The same relationship is true if power decreases. Each time you cut the power in half you have a 3 dB decrease. If you cut the power in half again, there would be a 6 dB decrease. dBs are only added or subtracted, they are never multiplied or divided. Example for decibel conversion. If a signal has a gain of 8000 ( 8000 times bigger), what is the gain in dB? The best way to solve this problem is to break up the gain of 8000 into its simplest factors as shown below. 8000 = 10 × 10 × 10 × 2 × 2 × 2 Now replace the multiplication of factors by the addition of dB. 8000 = 10 dB + 10 dB + 10 dB + 3 dB + 3 dB + 3 dB = 39 dB

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**Power Conversion Table**

Some common decibel values and power-ratio equivalents. Let’s compare the values between 10 dB. Plus and minus 3 dB and 9 dB is easy. Note that a drop of 1 dB reduces power by 20%. Also note that increasing power by 1 dB is an increase of 25%. The table shows the percentage error in our assumption

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**Basic Concept Wavelength () Length**

One of the important characteristics of the sinusoidal signal is its wavelength. In this figure we see that the wavelength of a sinusoidal signal is the distance between points representing a 360 degree phase shift. The wavelength is the velocity of the propagation divided by the frequency. Electromagnetic-energy waves have a length uniquely associated with each possible frequency. f (Hz) = ( Velocity of propagation)/ (m) or (m) = ( Velocity of propagation)/ f (Hz) The velocity in air is approximately ( 3.00 × 108 ) meters per second. (m) = {( 3.00 × 108 ) m/sec} / f (Hz) Example: what is the frequency of a 40 m RF wave ? f (Hz) = { ( 3.00 × 108 ) m/sec}/ 40.0 m = (7.5 × 106 ) Hz or = 7.5 MHz

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**εr = relative dielectric constant**

Wavelength () VC () = εr f Where: VC = velocity of propagation through air εr = relative dielectric constant f = frequency of oscillation This is the equation for finding the wavelength of a signal in a dielectric medium. Notice that the wavelength decreases as the frequency increases or when it passes through material with a higher dielectric constant than air.

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**Velocity of Propagation**

Electromagnetic energy travels at the speed of light. The velocity in air is approximately ( 3.00 × 108 ) meters per second. When the signal is traveling through another medium, such as coaxial cable, the dielectric properties of the material begin to slow down the signal. When traveling through dielectric material, the velocity is inversely proportional to the square root of the relative dielectric constant.

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**Time Domain and Frequency Domain**

An oscilloscope is used when we want to see how the signal varies with time, but this does not give us the full picture of the signal. In order to fully understand the performance of a system, we need to look at the signal in the frequency domain. Frequency domain is a graphical representation of the amplitude of the signal as a function of frequency. An oscilloscope can be used to view signals in the time domain and a spectrum analyzer can be used to view signals in the frequency domain. Looking at a signal in the frequency domain will give us more information than looking at a signal in the time domain. For example, a signal may look clean in the time domain but if we look at it in the frequency domain, it may include many other frequencies (harmonics).

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**Transmission Line Theory**

Must be applied when line lengths are > ( / 4 ) Standard lumped-circuit analysis can be applied when the line lengths are << ( / 4 ) When a transmission line is much less than 1/4-wavelength, the voltage seen at both ends of the line is essentially the same. If there are discrete devices such as resistors at both ends, the devices “see” the same voltage. The elements and circuit can be analyzed as lumped-circuit elements using conventional DC or AC theory. If the transmission line is 1/4-wavelength long, we find zero voltage at one end and a maximum or minimum voltage at the other end. The transmission line must now be analyzed using transmission line theory. A frequency that is usually given as the start of the microwave region is 1 GHz. If we calculate the wavelength of 1 GHz through space, we have lambda () equal to 30 cm. (m) = ( 3.00 × 108 ) / f (Hz) = ( 3.00 × 108 ) / (1.00 × 109 ) = 0.3 m = 30 cm Then 1/4-wavelength = (30 cm ) / 4 = 7.5 cm So when a frequency of 1 GHz is propagated along a transmission line of approximately 7.5 cm or longer, microwave transmission line theory will be needed in order to evaluate the circuit.

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Impedance The impedance of a transmission line can be complex Z = R ± jX If X is positive, it is called the inductive reactance If X is negative, it is called capacitive reactance Impedance plot in a rectangular coordinate The impedance as seen on a transmission line is the ratio of the voltage to the current at a defined point on the transmission line. From the above figure the absolute value of the impedance can be calculated by the Pythagorean formula, Z = (R1)2 + ( X1)2 and the angle of that impedance is given as tan 1 = X1/ R1

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**Different Types Transmission Line**

There are many different types of transmission lines and we will talk about three of them. Coaxial Waveguide Microstrip

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Coaxial Cable Coaxial Cable is the most common form of a transmission line. It consists of two conductors arranged concentric to each other and is called “coaxial” because the two conductors share the same center axis. The inner conductor will be solid or stranded wire, and the other conductor forms a shield. Coaxial cable can be bent and it has a relatively dependable match over a very wide frequency range. Characteristic impedance and frequency cutoff are two important properties of a coaxial transmission line.

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Waveguide Waveguide is a hollow, conducting tube, through which microwave frequency energy can be propagated. Here are four common shapes for waveguide. The most common is rectangular. Circular waveguide is often used when high power capability is needed. The single and double-ridge waveguides are usually used where a wider bandwidth is needed than is available in rectangular waveguide. Why Does Waveguides Exist? 1- Waveguide is normally less lossy than coaxial cable. 2- Fabrication of waveguide for high frequencies is easier than coaxial cable. 3- Waveguide can handle higher power levels than coaxial cable. Common Waveguides: Rectangular Double Ridge GHz WR GHz WRD750 GHz WR GHz WRD180 33-50 GHz WR22 40-60 GHz WR19 50-75 GHz WR15 60-90 GHz WR12 GHz WR10 90–140 GHz WR8 110–170 GHz WR7 140–220 GHz WR5 GHZ WR4 GHZ WR3

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**Microstrip Transmission Line**

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**Characteristic Impedance of Coax**

For a lossless line R=G=0 Note: The physical relationships between the inner and outer conductors and the dielectric material used will establish the impedance. Another type of coaxial line is the air line. An air line is a coaxial transmission line using air as the dielectric. Since the dielectric constant is one, the impedance is determined by the mechanical tolerance of the line. With tight mechanical tolerances, controlling the D to d ratio, the airline can be manufactured with excellent characteristic impedance control.

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**Characteristic Impedance**

Z0 = (138/ εR) Log (D/d) Where εR = Relative dielectric constant D = Outer conductor ID d = Inner conductor DD Consider an infinity long length of lossless coaxial transmission line. If an RF signal is applied, a current will flow which is equal to the applied voltage divided by the characteristic impedance, Z0, of the transmission line. The applied signal will travel down the line forever. Typically, Z0 might be 50 ohms. Next, remove a few feet of the transmission line. The remainder of the line is still infinitely long and still has an input impedance of Z0. The short length of line was previously terminated by Z0, the remaining length of the infinity long line. If we terminate the short length by an impedance equal to Z0, the current will remain unchanged; for the conditions all appear to be the same. All of the energy applied to the short length will be accepted and absorbed by the termination. Since the line is defined as lossless, the RF voltage remains constant as it travels along the line.

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**Propagation Modes of Coax**

Patterns set up by electric and magnetic fields. As the signal travels through a coaxial line, it sets up a pattern of electric and magnetic fields. Propagation mode describes the type of pattern which is present within the line. As the frequency increases, and wavelength decreases (approaching the diameter of the coax), alternate modes, or patterns, become possible. The transition from one mode to another is known as moding. The problem with moding is that it induces energy loss. This is due to more than one mode propagating the signal at the same time. The transition to an alternate mode is revealed by an abrupt increase in insertion loss ( about 3 dB) at certain frequencies.

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**Cutoff Frequency of 0.141 Cable**

The lowest frequency at which the next higher order mode can propagate is called the cut-off frequency of the next higher order mode. This is the equation for finding the frequency cutoff of a coaxial line. You can see that the dimensions of the cable have an inverse relationship to the upper frequency limits. This is the main reason for using smaller cable at high frequencies. Cutoff Frequency of Cable A popular semi-rigid cable used in the industry is the UT-141 cable. The term “141” refers to the outside dimension of the cable, which is 141 mils (0.141 inch). We can use the frequency cutoff equation to determine the upper frequency limit of the cable. Note that the frequency at which moding can occur is 33 GHz. This clearly demonstrates why cable of this size could not be considered for higher frequencies.

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**Velocity of Propagation**

In free space C = 3x108 m/sec Wavelength = λ = C/f Where f = frequency (Hz) Z The velocity of propagation of energy is equal to a constant times the speed of wave propagation in free space. This constant is known as the relative propagation constant and is a number less than one.

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**Relative Velocity Constant (k)**

k = (1/ εR) for Teflon: εR = 2.04 k = (1/ ) = 0.7 The relative propagation constant is a function of the relative dielectric constant of the material between the center and outer conductors of the coaxial transmission line is equal to K = (1/ εR) We can now calculate the distance for one wavelength at 1 GHz for a coaxial cable with a solid Teflon dielectric. λ = (CK/f) = [(.7 × 3 × 10 × 1010)/109] cm λ = 21 cm

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**Phase of The Signal at One Wavelength**

The phase of the signal at one wavelength intervals along the line will be in phase. In this instance λ0 is 21 cm at 1 GHz.

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**Well Matched Transmission Line**

If Z0 = ZL then P0 = PL No reflection Therefore PL = PI Analyzing a microwave signal propagated along a transmission line. Here we have the power traveling past Z0. Z0 represents the characteristic impedance of the transmission line. If ZL is equal to Z0, then the voltage drop across ZL is equal to the voltage drop across Z0; thus, all of the power that passed by Z0 is absorbed into ZL. Since all the power is absorbed into ZL, there is no residual power left on the transmission line. The line is said to be matched. ZL can be considered to be a perfect termination.

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**Poorly Matched Transmission Line**

If ZL ≠ Z0 then PL ≠ PI Reflection is present Therefore PL = PI - PR If ZL ≠ Z0 , then the voltage drop across ZL ( and thus the power absorbed by ZL ) is not equal to the input voltage. This mismatch causes some residual power to be sent back towards the generator. The line is now a mismatched line. This creates two waves of the same frequency traveling in opposite directions. By measuring the reflected power, we can obtain information on the impedance of the terminating impedance or device under test relative to the transmission line impedance.

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**Short at the end of the line**

Example Short at the end of the line The example shown assumes a short at the end of the line which produces a 100% reflection. The maxima are twice the incident voltage and the minima are zero. The magnitude of the reflection can be described as a standing wave ratio, Vmax SWR = Vmin In this case (with the short) the SWR = (2V/0) = . A shielded open would produce a similar pattern except that the sum of the incident and reflected voltage would be a maximum at the plane of the open. The magnitude of the reflection would be the same as that with the short. The SWR would again be infinite. Some years back the E field in the transmission line was sampled using a slotted line in order to determine SWR. This method is tedious and has lost favor. But many people still specify match in terms of SWR.

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**SWR Vs Impedance ZL 0, ZL and ZL Z0**

When ZL is a finite value other than 0 ohms, or Z0 ohms, VMax will decrease and VMin will increase. When ZL = Z0, VMax = VMin = V incident and V reflected = 0 SWR can be calculated from Z0 and ZL. Conversely ZL can be calculated from SWR except there will be two possible values. One > Z0 and one < Z0. If ZL > Z0 SWR = ZL/Z0 If ZL < Z0 SWR = Z0/ZL

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**VSWR Voltage Standing Wave Ratio (VSWR) Emax ER + EI VSWR = =**

Emin ER - EI ER G(reflection coefficient) = EI The voltage standing wave ratio (VSWR) is defined as the ratio of the maximum and minimum voltage on a transmission line (Emax /Emin ). Where: Emax is the maximum voltage on the line Emin is the minimum voltage on the line The VSWR describes the magnitude of the standing wave, which, in turn describes the amount of interaction between the incident and reflected signals. The reflection coefficient magnitude, (rho), is the ratio of the reflected signal to the incident signal, ER/EI . The reflection coefficient is a number between 0 and 1.0 which is a percentage of the energy that is reflected back to the source. more directly describes the magnitude of the reflected signal, while VSWR describes the results.

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**Reflection Terms & Relationships**

The chart above provides an easy way to convert between the three reflection terms. Note that Reflection Coefficient is like a percentage and is a linear term. With a Reflection Coefficient = 1 (Infinite SWR, 0 dB Return Loss), all of the signal is reflected and this is a very bad match. With a Reflection Coefficient = (20 dB Return Loss, 1.22 SWR) 10% of the signal is reflected. Typical for a cable – okay match. With a Reflection Coefficient = (40 dB Return Loss, 1.02 SWR) only 1% of the signal is reflected. This is very good match. With a Reflection Coefficient = .001 (60 dB Return Loss, SWR) only 0.1% of the signal is reflected. This is a nearly impossibly perfect match but can be realized with an expensive precision airline.

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Reflection In the picture above, the Test Device has an imperfect match. Because of the imperfect match, a portion of the Incident signal is reflected back to the Source. The magnitude of this reflected signal can be expressed in reflection coefficient or Return Loss.

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**Reflection Coefficient**

Reflection coefficient is the ratio of the reflected signal to the incident signal. ZL - Z0 ER/Ei = = || = ZL + Z0 The reflection coefficient is a vector which has both magnitude and phase information. The absolute value of the reflection coefficient ER ------= Ei Return Loss = -20 log (|| ) EMAX (||) VSWR = = EMIN (||)

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Mismatch Mismatch is a measure of the efficiency of power transfer to the load. The percentage of the power reflected from the Load. 0 dB return loss or infinite VSWR indicate perfect reflection by the load. Infinite return loss or unity VSWR indicate perfect transmission to the load. When two RF components are not perfectively matched, the RF signal will start heading back down in the direction from which it came, this is called mismatch or imperfect match.

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**Basic Measurements Transmission Loss/Gain = Pout/Pin**

Return Loss = Preflected/Pin Microwave component manufacturers and systems integrators need to make two basic measurements. They need to measure the gain or loss through their device and they need to measure the power that is reflected off their device. This reflected power is an indication of the device under test, relative to the characteristic impedance. If we are working in 50 ohms and we had a perfect match to 50 ohms on our device under test, there would be no reflected power.

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**Transmission Measurement**

Combining Signals Certain measurements and most error analysis requires knowledge regarding the summation of two signals. For example, knowing the amplitude (voltage) of two signals, what is the dB ratio of their sum and difference? Knowing dB amplitude of their sum and difference, what is the dB relationship between the two signals. Sometimes we need to know the true average value when we have a dB (log) display. By definition, V1 will always be larger than V2. As the phase of V2 varies with respect to V1 the magnitude of the sum will vary. The maximum value is simply V1 + V2 (in phase). The minimum is V1 - V2 (out of phase). If their relative phase varies at a constant rate, we obtain a ripple pattern when plotted as a function of time. If V1 is the signal that we want to measure and we are observing the sum of V1 plus V2, it is clear that the apparent average of the ripple pattern is the value of V1. Also, the value of V2 is equal to 1/2 of the peak to peak value of the ripple pattern. In this example we are observing voltage on a linear scale on the vertical axis. In practice, when we use a scalar network analyzer, we make sure observation on a log scale with a sensitivity of a constant number of dB per division. Now we no longer have a linear scale, but we can still make the same observation with a few calculations or from a look-up table.

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**Calculating dB Difference**

The peak to peak ripple, RdB, is equal to V1 + V2 20 log V1 - V2 We solve for V2 and substitute this value in the expressions for + dB and - dB. In the same manner we can write an expression for the dB difference. DdB = 20 log (V1/V2) and substitute expression (1) for (2). Let us assume that we have a peak-peak ripple on our display, and that the ripple is caused by an error signal smaller than the signal that we want to measure. We measure the ripple amplitude to be 5 dB ( RdB = 5 dB). Solving equations (2) and (3) yields dB and dB respectively. Solving equation (4) yields DdB = dB. We can subtract dB from the peak to get the true reading. The dB difference between our true signal and the error signal is 11 dB.

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Power Gain Gain is the ratio of the output power level of an amplifier to the input power level to that amplifier. Po Gain = Pi The term gain is a relative term and it is not a measure of some absolute level, or impedance, or frequency. Gain = Po/Pi This ratio is a number, and for gain this number is greater than one. Gain usually is expressed in decibels (dB). Gain (dB) = 10 log (Po/Pi ) For example, if Pi is mW and Po is 30 mW, Gain (dB) = 10 log (30mw/5mw) = 10 log (6) = 7.78 dB When Pi and Po are expressed in dBm (dB relative to 1 mW) then the math is easier. Gain = Po – Pi = 10 dBm – (-20 dBm) = 30 dB.

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**Transmission Measurement (Loss/Gain Measurement)**

Transmission Power Gain = 20 log (Vo/Vi) We have already defined transmission gain or loss as 10 log ( Pout/Pin ) of the DUT, but we can express it as 20 log ( Eout/Ein) in terms of voltage as well. If the DUT is an amplifier, we would have gain and the result would be a positive number. But if we had a loss, the result would be a negative number.

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**Making a Transmission Measurement**

Measure incident power going into the device. Measure the output power coming out of the device. The difference in power is transmission loss (or gain). Our objective is to accurately measure the power going into the DUT and the power coming out of the DUT. The difference in the two power levels is the transmission loss (or gain).

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**Measure Incident Power**

Using detector directly on the test port. To establish our transmission references, the DUT is taken out and the detector put directly on the test port. This not only measures the source flatness but also takes into account detector sensitivity variations. On the network analyzer you will see a fairly flat line when making this measurement. This is because the test port and the detector are fairly well matched. Using a detector with poorer match will increase the ripple in the display which is caused by the interaction of the incident power with that reflected from the detector. This is a problem because when the DUT is re-inserted, the electrical length changes. This results in new (and not calibrated for) phase relationships. The ripple magnitude thus becomes as error component for the measurement.

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Measure Output Power By inserting the DUT and attaching the detector to the DUT output, we measure how much incident energy passes through the device. By referencing this measurement to the calibration measurement, we can calculate how much power the DUT loses (or gains). With imperfectly matched devices you can imagine additional reflections existing which will cause a ripple pattern to appear on the CRT of the network analyzer. This will limit our ability to measure the transmission loss of the DUT.

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**Transmission Measurement Errors**

Calibration Error Test Port Match Detector Match Using Adapters There can be several sources of measurement error in Transmission measurements. We will discuss each in detail and learn how to calculate their contribution to measurement error.

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Calibration Error The calibration was performed with the detector directly measuring the power at the test port. The next step is to insert the DUT. When the DUT is inserted the electrical length changes and there is change in the phase relationship which will not cancel out.

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**Determining Calibration Error**

In our example the Calibration Error can be determined by adding the Detector and Source Return Loss and then using the graph at the left. Our detector has a 23 dB match and the source has a 20 dB match. Reading the chart at the left shows around +/- .06 dB. As you can see having a good source match and good detector match are important to achieving small measurement uncertainty. You can also use the RF Measurement chart to find the contribution of Calibration Error. Find the X dB below reference (which is 43 in this case) and read across to Ref + X dB and Ref – X dB.

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Test Port Match Error Test Port Match Error is caused by interaction of the test port match and the input match of the DUT.

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Detector Match Error Detector Match error is the additional interaction of (1) the DUT output with the detector and (2) the test port with the detector.

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**Calculating the Errors**

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Error Calculation

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Error Example One of the toughest transmission measurements to make is a low insertion loss DUT. In our example the DUT has only 1 dB of insertion loss (or transmission loss). Yet as you will soon see, the maximum errors can be about 0.4 dB on a 1 dB DUT. For the signal labeled “A” above the signal exits the source, passes through the DUT, a portion of it is reflected back off of the detector, passes through the DUT a second time and is reflected again off of the test port, and passes through the DUT again. For the signal labeled “B” above, the signal exits the source, passes through the DUT, is reflected off of the Detector and then is reflected off of the DUT’s output. For the signal labeled “C” above, the signal exits the source, is reflected off of the DUT’s input, then is reflected off of the test port (source) again.

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Error Calculation Add up all the dB values for each error contributor, then convert the sum to reflection coefficient and add the reflection coefficients together.

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Maximum Effect In our example the maximum effect of the measurement errors is determined by converting the DUT’s Insertion Loss to linear terms (1 dB = .891) and adding the measurement error reflection coefficient and then subtracting the measurement reflection coefficient. Convert the result back to dB. Use the Reflection Chart for these conversions. In this case our 1 dB DUT could measure anywhere between .66 dB to 1.38 dB. This is the worst case where all the error vectors are adding exactly in phase and exactly out of phase. In the real world this rarely happens, so we can use techniques to come up with a more realistic idea of the typical errors.

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RSS Using the Root Sum Square, we can calculate the more likely impact of the measurement error.

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Total Error Remember that we still have not added in the Calibration error.

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**What happens when you add an adapter?**

Many people do not realize how adapters can dramatically effect measurement errors. When an adapter is added to the test set up, the effective match of the Detector is reduced to the sum of the reflection coefficients of the Detector match and the Adapter match. Even a good adapter, like the one shown above, causes a 2.5 dB worse effective match. With a 15 dB adapter the effective match is: = = about 11.5 dB. Using the prior example the effect will be: A) 3(I.L.) + Detector/Adapter + Test Port = dB = dB dB B) I.L. + Detector + Output Match = 27.5 dB = .042 1 dB dB + 15 dB C) Input Match + Test Port + I.L. = 36 dB = .0158 15 dB + 20 dB + 1 dB Total = .0758 Maximum Effect DUT = 1 dB = .891 Plus error (.03 dB) Minus error (-1.77 dB) This is much worse than the error without the adapter

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Example 1 Your instructor will provide with a worksheet. This will give you an opportunity to get some practice determining measurement uncertainty in a typical measurement set-up.

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Example 2 Your instructor will provide with a worksheet. This will give you another opportunity to get some practice determining measurement uncertainty in a typical measurement set-up.

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**Improving Transmission Loss Measurements**

Use detectors with better match. Use attenuator pads or isolators between test port and DUT and detector and DUT to diminish magnitude of the error signals. When you are making transmission loss measurements, always use the best detector that you can find. The detector match is the primary error contributor. We can, however, improve source match by use of attenuators between the source output and the DUT. The errors, as will be seen in the transmission error analysis, do diminish as a percentage as the insertion loss of the DUT increases. If the DUT loss is changed from 1 dB to 10 dB, then measurement accuracy will be 10 ± .112 dB.

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**Return Loss Return Loss Measurements Uncertainty analysis**

Next we’ll examine how return loss measurements are made and explore measurement uncertainty associated with these measurements.

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**Return Loss Measurements**

Problem: How do you separate reflected signal from incident signal Let us look at a simple example of a signal source and an incident signal being reflected by a test device. We have talked about transmission loss and we have talked about return loss, but we have not talked about how you separate the two. There must be a way that one can measure the reflected signal, and it must be separated from the incident signal.

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**Solution to R L Measurements**

Solution: Directional Devices Definition: A directional device is able to separate either the incident or the reflected signal from the environment where both exist. You can do this by building a directional device of some sort. The directional device then would be able to separate either the incident or the reflected signal from the device being tested. Then we can very accurately analyze the effects of return loss.

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**Solution to RL Measurements**

Directional Devices: Couplers (Coaxial and Waveguide), Bridges, Autotesters The solution is a directional device. You might have seen coaxial and waveguide directional couplers, where the input power goes to one port, the RF circuit couples some energy off, and the rest of it goes through the coupler to the output port. The amount of energy that is coupled is defined as the coupling factor of the device. If some energy was reflected from the output port ( from the opposite direction), the amount of energy that would couple into this circuit would be a measure of the directivity of the coupler. In another words, you want the coupler to direct a certain amount of energy when it is traveling in one direction, but you would like for it to not couple any of the energy coming from the opposite direction. This then would give us the ability to separate the incident and reflected signals. A microwave bridge can do the same thing. You might refer to Anritsu Technical Review Volume I, No. 1, for a detailed discussion of the subject. Essentially, a bridge circuit provides you with the ability to measure the voltage at the detector, which is proportional to the reflection coefficient or SWR of the device connected to the test port. It is similar in principal to a Wheatstone bridge. Technically speaking a Bridge provides an RF output and you have to use an external detector. An Autotester is a Bridge with a built in detector.

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**Making a Return Loss Measurement**

Two requirements when measuring return loss Separation of incident and reflected signal Establish a 100% reflection reference In order to make return loss measurements, it is necessary to be able to separate the incident and reflected signals ( this is done with directional device discussed previously). In order to calibrate our system, it is also necessary to establish a 100% reflection reference. This is done by using our Anritsu compensated open/shorts during the measurement.

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**100% Reflection Reference**

For COAX two references exist: Open circuit Short circuit They are 180° out of phase For Waveguide two reference can be used short circuit and offset short Two 100% reflection references exist: open circuits and short circuits. Remember that an open circuit and a short circuit are 180 degrees out of phase. Since it is very difficult to to build a perfect open circuit, Anritsu manufactures a compensated open/short. We are then able to establish a reference that is 180 degrees out of phase. Averaging these two measurements eliminates the effects of any reference error. In waveguide situations it is more difficult, because only a short circuit available as a reference. If you leave the waveguide open, the waveguide will radiate and act as an antenna, which does not give you a usable reference.

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**100% Reflection Reference**

The Average of an Open & Short represents a “true” 100% reflection. This graph shows how proper calibration of the test port can significantly reduce errors. The best method is to average an open and a short, which are 180 degrees out of phase so they cancel each other, leaving the equivalent of full reflection voltage. This technique provides a better reference, and is encouraged for most coaxial measurements.

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**Return Loss Block Diagram**

This block diagram represents the basic elements of a return loss measurement system: a signal source, 100% reflection references, a directional device to separate signals, a detector, and a Scalar Network Analyzer. The source is a sweep generator. The directional device and detector is called an Autotester. The log amplifier and display function could be performed by the Scalar Network Analyzer.

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**Errors to Consider Directivity Test port match Termination error**

There are three main source of measurement error when making a return loss measurement.

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**Calculating Directivity**

Directivity = 20 log ( Vin/ Vout) dB Example: Vin = 1 Volt, and Vout = 10mV Directivity = 20 log ( 1/ .01) = 40 dB Directivity is the leakage (amount of incident signal) that appears when the directional device is terminated with a perfect load (also known as a termination). Nothing is perfect in the microwave world and a directivity of 40 dB is really quite good. This is a block diagram of a directional device with a perfect termination. If directivity is defined to be 20 log ( Ein/ Eout), then a 1-volt signal input with a 10 millivolt coupled signal output would represent a directivity of 40 dB. Directivity error, therefore, is the measure of how well the directional devices samples only in the proper direction. The more improper signal it sends out, the poorer it is as a directional device. Ultimately, directivity error is the final limitation of any return loss measurement.

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Test Port Match Test port match is the return loss of the connector that the DUT is attached to. Test Port Match Error then is the undesirable reflections that occur between the test port of the directional device and the DUT. In this block diagram, the small arrow labeled EM is the test port match error signal. The phasor diagram shows the reflection of the rotation of this vector, and the subsequent modulation of EO, ending up with the ripple pattern below. EM adds to and subtracts from EO, the DUT return loss signal, and must be considered in our error analysis.

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**Termination Error Errors in Return Loss**

Termination Error: The additional reflection that an imperfect termination causes. The last return loss measurement error we will consider is the termination error caused by reflections from an imperfect load. A perfect termination would absorb all energy, reflect nothing, and contribute no error. Perfect terminations do not exist. The primary specification of a termination is its return loss. 40 dB is a typical return loss for a good termination.

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Termination Error In this diagram, the reflections from our imperfect termination will modulate our DUT return loss signal. When making return loss measurements of two-port DUT’s, be sure to use the best possible termination to keep this error to minimum.

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**Calculating the Errors**

Directivity Error + Test Port Match Error + Termination Error ? Do it exactly the same way as you did transmission loss. Now that we have identified these three errors, how do we determine the accuracy of the measurement? The same way as transmission loss.

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**Calculating the Errors**

Calculate how far below the desired signal the error signal is (in dB). Convert the dB into linear (reflection coefficient) form. Use reflection chart or calculate. GE = log-1 [ -dB error/20] For worst case, add up all linear terms. Sum = GE1 + GE2 + GE3 First, determine the dB value for each error signal. Then convert these signals into linear form (reflection coefficients) and add them together. This will give you the worst-case measurement error, since it assumes that all reflections will add in phase or subtract out of phase. In reality, it is unlikely that this would ever happen, so the root sum square can be calculated, RSS = 2E1 + 2E2 + 2E3, which may be a more meaningful representation of the errors..

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**Calculating the Errors**

Effect on the measurement is the linear sum adding in phase or subtracting out of phase from the nominal return loss of the device under test. Measurement = GDUT ± GSUM In dB, meas. Max = - 20 log [GDUT - GSUM] Min = - 20 log [GDUT + GSUM]

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**Error Signal Return Loss (Reflection)**

Let’s look at an example of a return loss error calculation. The basic reflection error signals that we have discussed are: 1- directivity 2- test port interacting with the device under test (DUT) return loss, and 3- the error due to the termination (or detector in a simultaneous transmission/reflection measurement).

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**Calculating the Errors**

Autotester DUT Directivity = 40 dB (.01 G) Input/Output Match = 15 dB(.178 G) Test Port = 20 dB (.1 G) Insertion Loss = 1 dB Termination Detector Return Loss = 40 dB (.01G) Return Loss = 20 dB (.1G) If we consider these 3 basic errors, we find that with a 40 dB directivity SWR Autotester whose test port match is 20 dB, we can measure the DUT with the indicated accuracy. Note that a - The effect of the termination are isolated from the measurement signal by twice the insertion loss. b - The test port error is generated by the signal being reflected first from the DUT, then from the test port, and again from the DUT. Thus, this error is only important when testing devices having high reflection coefficients.

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**Return Loss Measurement Errors With Termination**

A) 2(I.L.) + Termination 2 dB + 40 dB = 42 dB (.008G) B) 2 (DUT) + Test Port 30 dB + 20 dB = 50 dB (.0032G) C) Directivity = 40 dB (.01G) Total Error = 0.021G

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**Measured Results For Using Termination**

DUT = .178G (15 dB) (1.43 SWR) Plus Total Error G .199G = (14.02 dB) ( 1.50 SWR) DUT = .178G (15 dB) (1.43 SWR) Minus Total Error G .157G = (16.08 dB) (1.37 SWR) This shows that this 15 dB device can be measured to within dB, and -.98 dB if a 40 dB termination were used.

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**Measured Results For Using Detector**

With Detector (as termination) A) 2 (I.L.) + Detector 2 dB + 20 dB = 22 dB (.079G) B) 2(DUT) + Test Port = 50 dB (.0032G) C) Directivity = 40 dB (.01G) .092G Measured Results DUT + Total Error .178G G = .270G (11.37 dB) (1.74 SWR) DUT - Total Error .178G G = .086G (21.31 dB) (1.19 SWR) If we substitute a detector for the termination, that error signal increases dramatically, because there is only 2 dB isolation ( twice insertion loss) between the autotester and the detector. Now the measurement uncertainty is dB, and -3.63dB. The moral of this story is: do not try to measure the return loss of a low insertion loss device by terminating with a detector, even with a well-matched detector like ours.

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**Error Signals Directivity = 40 dB Test Port Match = 20 dB**

Adapter = 36 dB DUT = 15 dB A- Effective Directivity Directivity = 40 dB (.01G) Adapter = 36 dB (.0158G) Minimum Effective Directivity Autotester = 40 dB = .01G Plus Adapter Error G .0258 = dB B- Effective Test Port Match Autotester = 20dB = (.1G) Adapter = 36 dB = (.0158) Minimum Effective Test port Match Autotester = 20dB = .1G Plus Adapter error G .1158G = dB A Major, and perhaps most common, mistake in error analysis is ignoring the effect that adapters have on accuracy. Remember that the adapter moves the reference plane (actual test port) from the SWR Bridge/Autotester to the output of the adapter. Therefore, any interaction between the directional device and the adapter becomes part of a directivity error. The first thing we should look at is what effect the adapter has on directivity by calculating “Effective Directivity”. This is done by simply adding the reflection coefficient of each. In this example, a 36 dB adapter lowers the 40 dB directivity to an “ Effective Directivity” of less than 32 dB. Remember that the effective directivity will always be less than the poorest component. If the adapter is only 20 dB, the effective directivity has to be less than 20 dB.

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**Input Match Errors Due to Sweeper Output and SWR Autotester Input Match**

Effective Input Match dB G Sweeper Input Match = .159 Autotester Input Match = .10 Effective Input Match = 11.7 dB .259 11.7 dB Effective Input IL = 6.5 dB For completeness, it is appropriate to consider the error due to the input or source match into the SWR Autotester or Bridge. Since the input arm of the Autotester has from 6.5 to 8.5 insertion loss, the test port is isolated from the signal source by 13 to 17 dB ( 2 × insertion loss). In most cases this is enough to reduce the error to insignificant levels. In this example of a return loss measurement, the error is . Taking this error into consideration, we measure the 15 dB device within about ± .75 dB. Without this error component being considered the total error is about ± .65 dB. Of this error, ± .5 dB is from directivity, so selecting the highest directivity available is the best way to reduce return loss error. Thus, except for the most precise measurements, source match error can be neglected when using a Bridge or Autotester,

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**Input Match Error Signal**

Error = DUT + IL + Input + IL + DUT dB G 15 dB dB dB + 15 dB Error Analysis dB G Directivity = = .01 Test Port 2(DUT) + Test Port = = .0032 Input = = Total Error DUT = 15 dB = .178 Plus Error .1931 = dB Minus Error .1630 = dB

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Example 3 Your instructor will provide you with a worksheet so that you can practice calculating measurement uncertainty for a typical return loss measurement.

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Example 4 One more example for you to try. This time with the detector as the termination.

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**Have We Forgotten Something?**

Instrumental Errors Connector Repeatability At this point, it is appropriate to point out that the errors we have discussed so far are only ones associated with interactions of the devices due to their non-ideal impedance characteristics. It is important to point out that we have conveniently forgotten about errors due to our test instruments (signal generator and network analyzer) and connector mating interface on the device we were testing. For extremely accurate measurements (under .5 dB absolute accuracy), it is necessary to consider these errors as well.

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**Instrumental Errors Signal source harmonics**

Network Analyzer/Detector deviation from logarithmic response (.01 dB per dB of measurement) Readout Error (manual .03 to .1 dB, automated .01 dB) Signal source power and frequency stability Instrumental errors are all related to non-ideal characteristics of the stimulus (generator) and receiver (network analyzer). The largest potential measurement errors resulting directly from the instruments themselves are caused by harmonics and by the deviation of the detector and the network analyzer amplifier from a logarithmic characteristic. The magnitude of the error caused by harmonics is a function of incident-power level, relative harmonic content, and phasing. At best, the effect is complex. Unfortunately, harmonics introduce error during both the calibration and measurement steps. If the harmonics are less than - 40 dBc, their effects are almost negligible. After harmonics, the nonconformity of the network analyzer/detector to a true logarithmic response curve is the most serious source of instrumentation uncertainty. As an approximation, ± 0.1 dB for each 10 dB of measured loss can be used in the error analysis. Measurements are also limited by the degree to which a minor graticule on which the display can be resolved by an operator (manual operation) or how well a digital readout can be read (manual operation) or the level to which that the input data is digitized (automated operation). Manual operation is limited to a range of about .03 to .1 dB. Automated operation generally can resolve down to .01 dB.

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**Connector Repeatability**

APC-7 Typically ± 0.02 dB N Typically ± 0.03 dB SMA Typically ± 0.04 dB K Typically ± dB V Typically ± dB The connector itself, its manufacturing and mating tolerances, can influence measurement accuracy. Based upon testing conducted at Anritsu, the repeatability of connector interfaces is on the order of .02 to .045 dB, depending on the connector type as shown. This repeatability can severely limit transmission loss measurement accuracy of low loss devices such as circulators, isolators, adapters, passbands of filters, etc.

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Summary This summary is intended to give you a feel for what you can expect when measuring insertion loss. The chart tells this: 1- Insertion Loss Measurements: Watch out for low loss devices. Errors can be quite large even when using good quality devices. Also, be careful when measuring devices with attenuation that drops the DUT output level below about - 40 to - 50 dBm. These levels are typically noise floor levels for modern diode detectors. 2- Return Loss Measurements: Be careful when the measured device approaches the directivity of the directional device or when measuring highly reflective devices. Errors can be surprisingly large. A final word, when in doubt, calculate the errors using the methods developed in this section. It may save time lost in analyzing ambiguous data.

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**S Parameters & VNA Measurement Fundamentals**

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**S Parameters S21 FORWARD TRANSMISSION Port 1 Port 2 a1 b2 a2 b1**

S11 FORWARD REFLECTION S22 REVERSE REFLECTION DUT S Parameters (Scattering Parameters) are shorthand for terms things like Forward Transmission. Instead of saying Forward Transmission we can say S21 and people in the industry know what we mean. A 2 port device has 4 S Parameters. Multiport devices have more S Parameters ( for example S31 is found on a three port device). S Parameters are usually associated with VNA measurements. S11 is Forward Reflection S21 is Forward Transmission S22 is Reverse Reflection S12 is Reverse Transmission S12 REVERSE TRANSMISSION

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S Parameters S Parameters (Scattering Parameters) are shorthand for terms things like Forward Transmission. Instead of saying Forward Transmission we can say S21 and people in the industry know what we mean. A 2 port device has 4 S Parameters. Multiport devices have more S Parameters ( for example S31 is found on a three port device). S Parameters are usually associated with VNA measurements. S11 is Forward Reflection S21 is Forward Transmission S22 is Reverse Reflection S12 is Reverse Transmission

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**S Parameters Defined S11= Forward Reflection (b1/a1)**

S21= Forward Transmission (b2/a1) S22= Reverse Reflection (b2/a2 ) S12= Reverse Transmission (b1/a2) All are Ratios of two signals - (Magnitude and Phase) S Parameters are the ratio of two signals. With VNAs we can see both the magnitude and phase of each signal.

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**Diagram for S-Parameters**

S Parameters are the ratio of two signals. With VNAs we can see both the magnitude and phase of each signal.

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Impedance Components The relationship between the reflection coefficient and the impedance on a transmission line As we mentioned before, the microwave impedance is expressed as a combination of two components: Z = R ± jX Where R is the resistive (or real) component and X is the reactive ( or imaginary) component If X is positive, it is called the inductive reactance If X is negative, it is called capacitive reactance We will look at all three components: resistive, inductive, and capacitive in the Smith chart.

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Smith Chart In the late 1930’s, Philip H. Smith presented a chart that could be used to analyze transmission lines without the use of long, involved equations. This chart became known as the Smith chart. At first glance it looks confusing, with numbers and lines and circles. But once you understand it, the chart is relatively simple. The Smith chart is based on two sets of orthogonal circles that represent microwave impedances.

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**Impedance Components The impedance components in the Smith chart are:**

The resistive components The reactive components A- Inductive B- Capacitive As we mentioned before, the microwave impedance is expressed as a combination of two components: Z = R ± jX Where R is the resistive (or real) component and X is the reactive ( or imaginary) component If X is positive, it is called the inductive reactance If X is negative, it is called capacitive reactance We will look at all three components: resistive, inductive, and capacitive in the Smith chart.

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**Constant Resistance Circles**

The first step in understanding the Smith chart is to look at the resistive portion of the chart. The above picture shows its pure resistance line, which goes through the center of the chart. Any points on this line are resistive only and contain no reactive components. The range of the resistance values is from zero ohms ( short) on its left to infinity (open) on the right. A perfect load is at the center ( Z0) of the resistive axis. Short is on the left, ZL = 0 Open is on the right, ZL = A perfect load is at the center, ZL = Z0

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**Inductive Reactance Circles**

The above picture shows the inductive reactance on the Smith chart which is when X, the reactive, is positive.

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**Capacitive Reactance Circles**

The above picture shows the capacitive reactance on the Smith chart which is when X, the reactive, is negative.

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Using Smith Chart This is an example to normalize a given impedance and find the point in the Smith chart. Given ZL = 40 + j42.5 and the system impedance Z0 = 50 ohm To normalize: ZL = (40 + j42.5)/50 = j 0.85 To find this point on the chart, first find 0.8 ohm on the resistance circle on the chart. Follow the circle in a clockwise direction, since the reactance is +j, until the 0.85 reactance circle is intersected which is shown as ZL. The VSWR circle can be found by using a compass. Put the point at the center of the chart and put the pencil point at ZL, then draw a circle as shown in the figure. The VSWR can be read at Point A, where the VSWR circle intersects the real resistance circle which it reads 2.5 in this example. The admittance can be found by taking the reciprocal of the impedance. To find admittance, draw a line from the impedance ZL through the center of the chart until the VSWR circle is crossed on the other side. This point is the corresponding admittance which in this example it is YL = j0.6 mhos. Fortunately, VNAs do the above for you.

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**What’s the difference between a VNA and a Scalar Analyzer?**

A Vector Network Analyzer not only measures the magnitude of the reflection or transmission, but it also measures its PHASE. A Scalar Network Analyzer uses a diode to convert energy to a DC voltage. It can only measure magnitude with limited dynamic range. A Vector Analyzer uses a tuned receiver followed by a quadrature detector, so phase can be measured. Ratio measurements and the benefits of the heterodyne process all contribute to over-all accuracy and dynamic range.

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What is phase? t These two signals have the same magnitude but are 90 degrees out of phase!

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Phase Using phase information, one can calculate the electrical delay through a device. Analyzing the variation of phase shift through a device with respect to frequency, one can calculate group delay. Group delay is one cause of distortion in voice transmission and bit errors in digital transmission systems.

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**What happens when two equal signals which differ by 180 degrees are summed?**

The resultant depends on their relative amplitudes If the amplitudes are equal - They completely cancel - This is not hypothetical - When a full reflection occurs at the end of a transmission line, all of the incident energy is reflected back to the generator This causes high standing waves Depending where you “look” along the line, you could see ZERO or Twice the loaded Voltage !!

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**How does a VNA display the S-parameters?**

Log Magnitude and Phase

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**Another VNA Display Mode**

Smith Chart

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VNAs and Calibration

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**VNA Test Set and Source a1 a2 b1 b2 Source Transfer Switch Power**

divider Rear Panel Reference Loops* a1 a2 40dB Step Attenuator** 4 Samplers Coupler b1 b2 Port 1 Port 2 DUT

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**Without calibration a VNA cannot make accurate measurements**

Calibration means removing errors Types of errors to deal with: Random Errors (i.e. Connector Repeatability) Cannot be calibrated out, due to randomness. Systematic Errors CAN be reduced via calibration Transmission and Reflection Frequency Response Errors Source and Load Match Errors Directivity and Isolation (Crosstalk) Errors

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**Error Vectors Once the error vector is known (Mag. & Phase)**

It can be vectorially added to the raw VNA measurement Resultant is the actual DUT performance! error coefficient raw VNA measurement actual DUT performance x

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Error Vectors

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Error Vectors

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How to Calibrate- To reduce the systematic errors for both ports (Forward and Reverse), a 12 term calibration is required. Open Short Load Through (OSLT) The most common coax calibration method Other calibration techniques LRL, LRM, TRM, Offset Short... Exercise Good Techniques for best results Practice/Care/Knowledge/Clean Parts

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**How does calibration work?**

The VNA measures KNOWN standards. It will compare the measured value to the known value, and calculate the difference. The difference is the error. It will store an error coefficient (Magnitude and Phase) at every frequency/data point, and use it when making measurements.

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**START HERE ALL MEASUREMENT ARE REFERENCED TO A STARTING POINT**

PHASE MEASUREMENTS BEGIN BY UNDERSTANDING WHERE THE REFERENCE PLANE IS POINT IS THE REFERENCE PLANE

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**WHY MUST WE MEASURE PHASE???**

ERROR CORRECTION REQUIRES THAT WE HAVE PHASE AND MAGNITUDE INFORMATION – EVEN IF WE ARE ONLY CONCERNED WITH MAGNITUDE DURING TESTING! All four S Parameters are interdependent, so we must constantly reverse to compensate for Source Match, Load Match, Directivity, Frequency Response (Reflection), Frequency Response Transmission, and Isolation.

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**Systematic Error Transmission Frequency Response**

Reflection Frequency Response Source Match Load Match Directivity Isolation (Crosstalk) Reduced by Calibration These Six Terms on both Ports, yield 12 Term Error Corrected Data.

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**Corrected S-parameters**

Yuk – this is for the advanced class. Makes you appreciate what a modern VNA does for you though.

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**Calibration - (Open, Short Load, Thru)**

The most common calibration type is the OSL. Open Infinite Impedance Voltage Maximum O degree Phase Reflection Reflection Magnitude = 1 Load (Broadband) 50 Ohms (match) Reflection Magnitude = 0 Short Zero Ohms Impedance Voltage Null 180 degrees Phase Reflection Reflection magnitude = 1 Through Test ports connected together for transmission calibration measurement

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**Calibration – OSL Sliding Load**

Due to the difficulty of producing a high quality coaxial termination (load) at microwave frequencies, a sliding load can be used at each test frequency to separate the reflection of a somewhat imperfect termination from the actual directivity Broadband measurements required high accuracy must use 12 Term sliding load calibration Due to the difficulty of producing a high quality fixed coaxial termination at microwave frequencies, a sliding load can be used at each test frequency to separate the reflection of a somewhat imperfect termination from the actual directivity. At any single frequency, moving the sliding termination with respect to the measurement plane produces a complete circle when the sliding element is displaced on-half wavelength of the test frequency. Its reflection coefficient magnitude remains constant but the phase of the coefficient changes. The radius of that circle is the actual reflection coefficient of the sliding termination, and the center of the circle is terminated by the actual directivity of the test setup and the geometry of the air line within the sliding load. Thus the critical specifications for the sliding load assembly are the mechanical dimensions (impedance) of the connector, of the transmission line between the measurement plane and the termination, and that the termination maintains a constant reflection coefficient magnitude at all positions.

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**VNA Measurement Uncertainties**

The quality of a VNA measurement can be affected by the following : The Quality of the Calibration Standards Error Correction Type used – 12 Term, 1 Path 2 Port, and etc. Dynamic Range of the measurement system (VNA) – IFBW, Averaging and etc. Cable stability and Connector repeatability

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Uncertainty Curve Uncertainty Curves found in the Instrument Technical Data Sheet are primary related to test port characteristics associated with a given calibration kit plus the noise performance associated with the VNA. In other words, these charts are based upon very specific calibration and measurement conditions. Conditions are usually described in footnotes such as: 12 Term sliding load calibration required IF Bandwidth is 10 Hz Averaging used is 512 If your measurement set up matches the above conditions, then you can use the Uncertainty Curve chart to approximate the uncertainty of your measurement. For example, a device with an insertion loss of 10 dB is being measured. The measurement uncertainty is approximately ± 0.2 dB at 2 GHz.

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Exact Uncertainty A Windows based program is available to help obtain the uncertainty data that is appropriate for the customer’s specific application. CDROM part number Application Note

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**Measurement Uncertainty Exercise**

Assuming the VNA is set up for transmission measurement under the same conditions as specified in the Technical Data Sheet and you are going to measure a device with 30 dB loss, what is the measurement uncertainty at 2 GHz? Your answer is _______________ What is the measurement uncertainty at 40 GHz?

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**Common Microwave Devices**

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**What do our Customers manufacture?**

Amplifiers Mixers Power Dividers Power Splitters Combiners Couplers Circulators Isolators Attenuators Filters

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Amplifier An Amplifier is an active RF component used to increase the power of an RF signal. Four fundamental properties of amplifiers are: Input/Output Matches Gain Noise figure Linearity - 1 dB Compression point Small signal in Big signal out RF signals need to be made bigger as they move from place to place just like driving a car. When you drive a car from place to place using gas, and when you run low in gas, you fill up. An RF amplifier is a filling station for RF signals. RF signals move around from place to place (either in air or along a conductor), when they need a boost, amplifiers are used to give them a power boost.

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Match and Gain Use the Transmission/Reflection Measurement mode of the VNA to measure these parameters: Input match – S11 Output match – S22 Gain – S21 Gain, Input match and Output match of an amplifier can be measured using the Transmission/Reflection mode of the Vector Network Analyzer.

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**Noise We are interested in specific man-made signal**

But there are some unwanted signals combined with our desired signal. Thermal Noise Noise is any signal that is not the one in which we are interested. There are many unwanted signals occurring naturally which would combine with our desired signal. Noise can be divided in two classes: external noise and internal noise. External noise includes interference from signals transmitted on nearby channels, man-made noise generated by faulty contact switches, by automobile ignition radiation, fluorescent lights, and natural noise from lightning, and electrical storms. The external noise can be minimized or even eliminated with proper care. Internal noise results from thermal motion of electrons in conductors, random emission, and diffusion or recombination of charged carriers in electronic devices. The effect of the internal noise can be reduced with proper care but it can never be eliminated. Noise is one of the basic factors that sets a limit on the rate of communication. Thermal Noise is produced by random motion of free electrons in conductors and semiconductors. This kind of noise increases as the temperature increases.

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**Noise Measurement There are many ways to express noise.**

Noise may be expressed in Noise Factor which is defined as the input signal-to-noise ratio to the output signal-to-noise ratio. Si/Ni F = So/No Noise Factor is the ratio of the total output noise power (thermal noise plus noise added by the stage) to the input noise power when the temperature is at the standard temperature of 290 K (17 º C).

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Noise Figure Noise can be expressed in Noise Figure which is the logarithmic equivalent of Noise Factor. Si/Ni NF = 10 log So/No The Noise Figure measures the reduction of a signal-to-noise ratio by the network under consideration. NF = 10 log (Si/Ni / So/No) where: NF is the noise figure in decibels. Si/Ni is the input signal-to-noise ratio. So/No is the output signal-to-noise ratio.

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**Noise Figure Measurement**

Traditionally, noise figure of an amplifier is measured using a Noise Source and a Noise Figure Meter. MS462XX Series Scorpion Vector Network Measurement System has built-in Noise Figure Measurement capability from 50 MHz to 6 GHz. In addition to Noise Figure, the MS462XX can also display Insertion Gain, Available Gain, and Y-Factor.

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**Output power VS Input power of an amplifier**

Linearity Linearity is a measure of how the gain variations of an amplifier as a function of input power distorts the fidelity of the signal. Output power VS Input power of an amplifier A tiny change in the shape of the RF carrier which contains information, will cause a loss of some information. Referring to the above picture, as the input power to an amplifier increases, the output power from the amplifier increases until the point A. Everything up to point A is known as the linear region of an amplifier. Notice that increasing the input power beyond point A, the output power no longer rises. After point A, the amplifier is said to be in saturation and enters non-linear region. Also, Point A called 1 dB compression point. One method of measuring an amplifier’s linearity is by its intercept point which is also called the third-order intercept point. The higher the intercept point, the more linear the amplifier. For example, an amplifier with a 40 dBm intercept point is more linear than an amplifier with a 30 dBm intercept point. If the input power of the amplifier increases further, eventually a point is reached where the output power of the amplifier increases rapidly, as shown. This point is referred to as the 911 point (joke).

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**1-dB Compression Point Input signal (dBm)**

The above picture represents the output signal verses the input signal of an amplifier. The dotted line represents the theoretical output level for all the values of input signal and the slop of the line represents the gain of the amplifier. As the amplifier saturates ( solid line), the actual gain begins to depart from the theoretical at some level of the input signal (Pin1). The -1 dB compression point is that output level at which the actual gain departs from the theoretical gain by -1 dB. The -1 dB compression point is the point at which intermodulation products begin to emerge as a serious problem. Also, harmonics are generated when an amplifier goes into compression.

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Gain Compression Traditionally, power meter is used for this measurement – tedious procedure VNA can now be used – very quick and simple Two VNA approaches are available: Swept Frequency Gain Compression Swept Power Gain Compression Using power meter to measure Gain Compression is a tedious procedure. When using a VNA, two approaches can be used: Swept Frequency Gain Compression Swept Power Gain Compression

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**Swept Frequency Gain Compression**

Swept Frequency Gain Compression function allows the user to obtain a normalized amplifier response as a function of frequency at Pstart and manually increases the input power while observing the decrease in gain as the amplifier goes into compression. This permits the user to easily observe the most critical compression frequency of a broadband amplifier.

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**Swept Power Gain Compression**

Swept Power Gain Compression test is done at a CW frequency. The input power will be increased with a step sweep starting at Pstart and ending at Pstop. Pstart, Pstop and step increment are user defined. This enables the user to observe the conventional Pout vs. Pin presentation or a display of phase vs. Pin. The VNA permits the user to select up to ten frequencies for swept power gain compression tests.

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**Third-order Intercept Point (TOIP)**

The third-order intercept point is the most important specification of a receiver’s dynamic range performance. Because this point predicts the performance regarding intermodulation. Third-order and higher intermodulation products (IP) are usually very week and do not exceed the receiver noise floor when the receiver is operating in the linear region. However, as input signal levels increase, forcing the front end of the receiver toward the saturated nonlinear region, the IP emerges from the noise as it shown in the graph. This begins to cause problem and new spurious signals appear on the band.

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**Third-order intercept point (TOIP)**

This is a plot of the output signal Vs the fundamental input signal. The theoretical output that would be produced if the gain did not clip is shown as the dotted gain line continuing above the saturation region. The third-order products in the output signal emerge from the noise at a certain input level and increase as the cube of the input level. Therefore, the slop of the third-order line increases 3 dB for every 1-dB increase in the response to the fundamental signal. The output response of the third-order line saturates the same as the fundamental signal, but the gain line can continue to a point where it intersects the gain line of the fundamental signal. This point is the third-order intercept point (TOIP).

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**Intermodulation Products**

Understanding the dynamic performance of the receiver requires knowledge of intermodulation products (IP). How intermodulation is created? What are the intermodulation products? Whenever two signals are mixed together in a nonlinear circuit, a number of products are created. The formula for intermodulation products is (mF1 ± nF2), where m and n are either integers or zero. Signals are mixed either in the mixer stage or in the receiver front end or in the RF amplifier if the amplifier is overdriven by strong signal. The corrosion on antenna connections and rusted antenna screw terminals may cause IPs. Given input signal frequencies of F1 and F2, the main IPs are: Second order F1± F2 , Third order 2F1± F2 and 2F2± F1 Fifth order 3F1± 2F2 and 3F2± 2F1

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**Intermodulation (Continued)**

Frequencies causing problem Overdriven amplifier or receiver The most serious frequencies are the third-order frequency signals ( 2F1- F2 and 2F2- F1) because they are close to the RF frequency. Notice that one of the third-order frequencies ( 3F1- 2F2) is on the same frequency as the desired signal. It could cause interference if the amplitude is sufficiently high. When an amplifier or receiver is overdriven, the second-order content of the output signal increases as the square of the input signal level, and the third-order responses increase as the cube of the input signal level. Example: Consider two signals F1= 10 MHz and F2= 15 MHz are mixed together. The second-order IPs are 5 and 25 MHz. The third-order IPs are 5, 20, 35, and 40 MHz. The fifth-order IPs are 0, 25, 60, and 65 MHz. If any of these signals are inside the passband of the receiver, then they can cause problems. If the receiver is tuned to 5 MHz, then a spurious signal would be found from the F1- F2 pair. Intermodulation distortion (IMD): The unwanted mixing of two strong RF signals that causes a signal to be transmitted on an unintended frequency.

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**IMD/TOI Measurement Setup**

MS462XX Scorpion Vector Network Measurement System with Option 13 Intermodulation Distortion (IMD) Measurement Capability makes it easy to measure Intermodulation Distortion (IMD) or Third Order Intercept (TOI) of a test device.

146
IMD Measurements For IMD Measurement, two options are available on Scorpion: CW Receiver Mode Swept IMD measurement mode CW Receiver Mode will display the measured result similar to that seen on a spectrum analyzer. In Swept IMD Measurement mode, the system receiver measures both tone and the two IMD products at each sweep point.

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TOI Measurement TOI Measurement setup is similar to IMD measurement. It includes one extra step during calibration. Receiver Cal is required for TOI measurement.

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Mixer A Mixer is a three-port component used to change the frequency of one of the input signals. Fundamental properties of mixers are: Conversion gain/loss Port Match Isolation Intermodulation Distortion (IMD)

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**Conversion Gain/Loss, Isolation & Port Matches**

Traditionally, mixer analysis required more than one test instrument. MS462XX Scorpion Vector Network Measurement System with second source and third port options allows the user to measure isolation, match and conversion gain/loss using a single instrument.

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Mixer IMD Measurement This configuration allows characterization of IMD products (both upper and lower products versus frequency). In addition, the VNA can calculate the third order intercept point (TOI or IP3).

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Power Divider A Power Divider (also called three-resistor power splitter) is a bi-directional device that equally divides an RF signal with a good match on all arms. Input Output 1 Output 2 The three-resistor power splitter is used in comparison measurements where it is necessary to divide power equally on a uniform transmission line. The three-resistor power splitter must be used for simple power division.

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Power Splitter A Power Splitter (also called two-resistor power splitter) is a passive RF device that equally divides an RF signal into two RF signals Output 1 Input Output 2 The two-resistor power splitter is used to improve the effective output match of microwave sources through either a leveling loop or a ratio measurement. The two-resistor power splitter must be used in leveling ratio measurements.

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Combiner A Combiner is a passive RF device used to add together, in equal proportion, two or more RF signals.

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**Coupler Directional coupler Bidirectional coupler A C B**

Coupler is a passive RF component in which the input signal is split unevenly and the smaller signal is siphoned off to be used somewhere else in the system. Coupling is the amount, expressed in dB, that is coupled down from the input. Typical values are 6, 10, 20, and 30 dB. How Couplers work: A signal enters the coupler at point A (see block diagram above) and makes its way to point C. Along the way, part of the signal is siphoned off and brought out at point B. Directional Coupler is an RF component that only works in one direction. Bidirectional Coupler is an RF component that works equally well in both directions. It can be referred to as dual-directional.

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**RF Hybrid Coupler The RF hybrid coupler is a device that will either**

(a) split a signal source into two directions or (b) combine two signal sources into a common path. Consider a situation when RF signal is applied to port 1. This signal is divided equally and flowing to both ports 2 and 3. Since the power is divided equally, the hybrid is called a 3 dB divider, because the power level at each adjacent port is one-half ( -3 dB) of the power applied to the input port. One general rule to remember about hybrids is that opposite ports cancel. It means that the power applied to one port in a properly terminated hybrid will not appear at the opposite port. In the case above if power is applied to port 1, no power will appear at port 4.

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**Applications of hybrids**

Combining two signal sources The hybrid can be used for a variety of applications where either combining or splitting is required. In case of above picture, two signal generators are connected to the opposite ports of a hybrid ( ports 2 and 3). Power at port 2 from signal generator 1 is canceled at port 3, and power from signal generator 2 (port 3) is canceled at port 2. Therefore, the signals from the two signal generators will not interfere with each other. In both cases the power splits two ways. For example, the power from signal generator flow into port 2 and splits two ways. Half of it ( 3 dB) flows from port 2 to port 1 and the other half flows from port 2 to port 4. Similarly, the power from signal generator 2 applied to port 3. It splits into two equal portions, with one portion flowing to port 1 and the device under test and the other half flowing to the dummy load.

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**Circulator and Isolator**

A circulator is a passive junction of three or more ports in which the ports can be accessed in such an order that when power is fed into any port it is transferred to the next port, the first port being counted as following the last in order. An isolator is a 3-port circulator with the third port terminated with a load so that power can only be transferred in one direction from the first port to the second port.

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Multi-port Devices The 3-port and 4-port MS462XX Scorpion VNMS provides an easy measurement solution for multi-port devices such as Power Divider, Power Splitter, Combiner, and Coupler.

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Attenuator An Attenuator is a RF component used to make RF signals smaller by a predetermined amount, which is measured in decibels. There are two types of attenuators: fixed and variable.

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Dynamic Range Dynamic Range is basically the difference between the maximum and minimum signals that the receiver can accommodate. It is usually expressed in decibels (dB). It is essential that the measurement instrument has sufficient dynamic range to accurately characterize an attenuator. VNA usually has two dynamic range specifications. Receiver dynamic range is the difference of the 0.1 dB Compression level (maximum signals input to the receiver) and the noise floor (minimum signal that the receiver can accommodate). System dynamic range is the difference of port 1 power and the noise floor.

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**Attenuator Measurements**

The above plot shows a transmission measurement of a 90 dB attenuator on a VNA using the default IFBW of 1 kHz and no measurement enhancements in both calibration and measurement. You can see that the noise floor of the receiver of the VNA interferes the measurement.

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**Attenuator Measurements**

The above plot shows a transmission measurement of the same 90 dB attenuator on a VNA using the IFBW of 10 Hz and 512 Averaging in both calibration and measurement. You can now see the transmission characteristics of the attenuator as the noise floor of the receiver of the VNA is now further from the measured signal.

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Filter A Filter transmits only part of the incident energy and may thereby change the spectral distribution of energy: High pass filters transmit energy above a certain frequency Low pass filters transmit energy below a certain frequency Band pass filters transmit energy of a certain bandwidth Band stop filters transmit energy outside a specific frequency band

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Filter Measurements The built-in Filter Parameter Measurement function in Anritsu VNA makes it easy to determine the filter properties such as 3 dB bandwidth, Q factor, and etc.

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Chapter 13 Transmission Lines

Chapter 13 Transmission Lines

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