Overview of Mixer Measurements

Overview of Mixer Measurements
Joel Dunsmore Solution Architect – Wireless Business Unit June, 2002 Some additions by Doug Rytting

Agenda Mixer Characteristics Traditional Mixer Measurement Techniques
New Concepts in Mixer Characterization Test Results Comparison & Complete Mixer Measurements Image Mixer Appendix The agenda today will cover several topics: General mixer characteristics will be introduced, so that we have a common set of terminology. Common methods currently in use will be presented, and the disadvantages of each will be discussed. A new concept for mixer characterization will be presented, and a new measurement system utilizing this technique will be introduced. Results of measurements with this system will be presented, and compared with other mixer measurement techniques. We will also describe the comparison mixer measurement technique and a proposal of how to make complete mixer measurements with no calibration assumptions. The appendix will describe the modifications needed when measuring image mixers.

Mixer Characteristics
Conversion Measurements Magnitude Response Phase Response Group Delay Input Match Output Match Isolation Spurious Mixing Products The traditional measurements made on mixers are conversion loss, input and output match, port isolation and spurious mixing products. This paper will concentrate on conversion and match measurements. The conversion measurements include magnitude (or amplitude) response, as well as phase response and group delay.

Mixer Conversion Measurements
Conversion gain is the ratio of desired-image power to applied input power Since the input and output frequencies are not the same, the definition of conversion phase can be confusing. We define the conversion phase as the phase shift of the output, were it synchronously reconverted to the input frequency with an ideal (zero phase shift) converter. frequency power level Conversion loss Amplitude conversion gain is easy to understand, it is the ratio of desired-image power to applied input power. Some common problems with amplitude response measurements are dealing with the non-ideal match of the mixers and test systems, which can distort the amplitude response. Also, some measuring systems do not have tuned receivers, and are therefore susceptible to errors due to undesired Images, LO leakage, and spurious responses.

Measuring Conversion Phase and Group Delay: AM Technique
Gd = - fe ¸ (360 * fmod) Phase Detector AM Modulator RF LO DUT Measure phase between two demodulated signals Sweep fmod The group delay of a mixer is most easily understood as the envelope delay. One well known method to test envelope delay is to AM modulate a signal, and measure the phase shift of the AM envelope (phase envelope) and from that and the modulation frequency, calculated the group delay. While this is intuitively easy to understand, this method has many problems that make it not practical in many cases. Errors can be introduced if the envelope has any distortion. Noise and non-linearities in the mixer-under-test will cause additional difficulties in the measurement of the phase shift of the envelop. This technique can only be used over a limited dynamic range, as the behavior of the detectors varies greatly over power. And finally, this technique only supports group delay measurements, and cannot be used for phase measurements of mixers. A final limitation is that the mixer must be filtered or the undesired image will also be detected.

Measuring Conversion Phase and Group Delay: FM Technique
Gd = - fe ¸ (360 * fmod) Phase Detector Demod Frequency Modulator RF LO DUT Demod Measure phase between two demodulated signals Sweep fmod Another well known method to test envelope delay is to frequency modulate a signal, and measure the phase shift of the demodulated envelope (phase envelope) and from that and the modulation frequency, calculated the group delay. This technique works better than the AM technique. However it requires a very accurate modulator and demodulators that have no AM to PM conversion. Many times the demodulator will limit the dynamic range of the measurements. Also this technique does not measure the phase shift of the DUT. Neither the AM or the FM technique can be error corrected for match or other microwave systematic measurement errors. However, this technique is very useful if the source and receiver are not located close to each other such as in satellite link measurements.

Up/Down Conversion with Equal Mixers
Requires Image filter Requires two matched mixers Mixers must be reciprocal Assume that Mixer1 = Mixer2 Must remove filter effects Must have accessible (or identical) LOs A second technique for determining the phase and group delay response of mixers is to use a pair of mixers, that are matched, and one of which is reciprocal. By reciprocal, we mean that the up-conversion loss is the same as the down-conversion loss. By using the two mixers back-to-back, the input frequency and the output frequency are the same. Now, normal network analysis techniques can be used to determine the amplitude and phase response of the mixer pair. A filter is required to remove the unwanted image, so that it is not re-converted to distorted the response from the desired image. The filter response must be removed from the pair response, and the mismatch between the filter and the mixers can cause additional uncertainty. Further, it is required that the LO’s be identical to both mixers. This is a severe limitation for mixers with an embedded LO. Finally, the assumption that the mixers are matched as well as reciprocal an irreducible source of error.

Three Mixer Technique Described by Clark, et al, in Microwave Journal, Nov 1996* Requires 3 mixers, One of which MUST be reciprocal Requires filtering of images Does not correct for mismatch between mixers Must remove filter effects Mxr A Mxr B Mxr C Mxr A Mxr C Mxr B Recently, Clark, et al, published a method whereby the assumption that the mixers pair are matched is removed. This method has all the same limitations as the previous slide, except the matched assumption. In addition, since three measurements are needed, and there can be filter and mixer mismatch in each measurement, there exists a strong likelihood that additional errors will occur. There are two irreducible limitations in this measurement method: At least one mixer must be reciprocal, and the image of the mixer must be able to be filtered out. *US Patent 6,064,694

New Concept in Mixer Characterization (Patented)
Requires a Reciprocal Calibration Mixer Requires an image filter for Calibration Mixer No other restrictions Currently supported in the Agilent PNA family External or Internal LO source Ref Standards A new method developed by the author eliminates most of the sources of errors of previous methods, while maintaining only two of the restrictions. The first restriction is that the undesired image be able to be filtered out. The second restriction is that the mixer be reciprocal in response. These are two of the restrictions of the previous methods, but this method does allow removing the effects of the filter, reduces the number of connects (and their attendant sources of error), and works for mixers with embedded, internal or external LO’s. Further, when combined with a VNA measurement system, even these limitations can be removed through a two step process. IF Filter

Mixer Calibration: Only calibrated reflection measurements are made.
RF signal is reflected off the input of mixer: does not change with load. IF + signal is converted and then reflected off image filter: does not change with load IF – signal is converted, passes through the IF- filter reflects off load: Changes With Load The key to this new concept is to look at a reflection measurement of a reciprocal mixer, and analyze the content of the signals. In this case, the mixer is a down converter. We identify the input signal as “RF”, and the output signals as “IF+” to represent RF+LO and “IF-” to represent the desired signal RF-LO. Let’s review what happens when we put a variety of loads on the output of the mixer. Note that the RF signal is not affected by the load, as the “IF-” band pass filter has a constant (high) reflection at all signals other than the “IF-” signal. Likewise, the IF+ signal is unaffected by the load, and it’s contribution to the the total RF signal going back to the VNA is likewise unchanged. Note that the “IF+” signal will be reconverted by the LO to the RF frequency, and that this final RF level will include twice the conversion loss of the mixer. The “IF-” signal will pass through the filter, reflect off the load, pass back through the mixer and be up-converted to the RF frequency, again with twice the conversion loss. All of these signals add to what will be measured in a reflection (S11) measurement of the mixer, but only the portion attributable to the IF- signal will change with the load impedance. In all of these measurements, we assume the VNA has been calibrated for reflection measurements, so that there are no errors associated with the VNA port characteristics.

Measure Mixer+Filter and Open
Here is a measurement of the S11 of a mixer, with an image filter. In this case we have selected measurement range to be greater than the filter response, to easily see the edges of the filter.

Measure Mixer+Filter and Open
This shows the three composite terms of the reflection signal, along with a fourth term, which represents the re-reflection of the IF- image off the load, and back off the output match (or S22) of the mixer under test. The open measurement is the vector sum of these terms. This represents one frequency of the previous plot. The IF- reflection is the conversion loss of the mixer (as the Gamma Load =1 for an open), and fourth term, representing output mismatch, can be reduced to S22 as again, the Gamma Load is 1.

Measure Mixer+Filter and Short (with Open still shown)
This shows the reflection measurement of the short (overlaid with the open). The fact that there is a large variation between the open and the short will be shown to be due to a large error term associated with the S22 or output match of the mixer.

Measure Mixer+Filter and Short
This vector plot shows how the terms combine to give the short measurement. Note in this case that the RF and IF+ reflections are not changed. The IF- reflection has a changed sign by 180 degrees, and the Gamma Short is –1. However, notice that the fourth term S22 times Gamma Load squared, is in the same direction as for the open. That is because Gamma Short is –1, and the squared term is 1, just as in the open case.

Measure Mixer+Filter and Load (with Open and Short still shown)
This plot shows the load response, notice that is is nearly in the center of the open and the short. If the actual open, short and load were ideal, the load response would be identically equal to the average (in dB) of the open and the short.

Measure Mixer+Filter and Load
Here is the plot of the load measurement for the same frequency as in the previous cases. Since Gamma Load = 0, there is no IF- term, and no term associated with the S22 times Gamma Load.

From the corrected measurements a 1-port error model is extracted
By Definition, S11 = EDF, also called D ESF = Mixer S22, also called M ERF = Mixer S21 * Mixer S12; Mixer S21 is also called T Mixer S12 is also called T2 Error terms include effects of filter and mixer The breakthrough for this method is recognizing that these measurements have a close corollary with the 1-port error model. In this case, the mixer S11 (also called D) maps to the EDF (Forward Directivity) error term of the 1-port model, the mixer output match S22 (also called M) maps to the ESF (Forward Source Match) error term, and the two-way response of the mixer (S21*S12) maps to the ERF (Forward Reflection tracking) error term. In notes that follow, we distinguish the mixer forward conversion as T1 (for first transmission term) and the reverse conversion as T2 (for the second transmission term). For the reciprocal mixer condition, T1=T2.

Calculate T1(mixer S21) Take the square root of ERF (not so easy)
Mag of mixer S21 is easy Phase of mixer S21 is more difficult Complex phase has two roots To choose the proper root: Un-wrap phase Use delay to project DC phase Offset phase by DC phase (assume phase = 0 at DC) Divide phase by 2 Re-wrap phase (easy, express in polar form) We call this result T1 which is also equal to T2 To get the conversion gain magnitude is easy, assuming S21=S12, by taking the square root the the ERF term. Getting the phase response is a little more difficult. The square root function applied to phase is really dividing the phase by 2. However, the phase wraps every 360 degrees so dividing by 2 will yield the wrong result. For example, the max phase is 180 degrees, so divided by 2 the max phase is 90 degrees, but that does not represent the real situation where the conversion phase can go to 180 degrees. Instead, what is needed is to un-wrap the phase (sometimes called expanded phase), then shift the first point phase reference to the proper offset value (and likewise shift all the other points). This shifted value is found by finding the delay (or phase slope) around the first point, and projecting it back to the zero frequency. The value at zero frequency is the offset for the phase trace. Once this is applied, the resulting trace is divided by two. Converting from the polar representation to the real/imag representation will re-wrap this new phase response.

If your mixer is reciprocal: Done
If your mixer is reciprocal: Done! If not, you can use the reciprocal cal mixer to calibrate a VNA Set up a VNA with Up/Down converter Step One: Using normal VNA techniques, obtain ERF, ESF, and EDF (all at RF Frequency), and ELF (at IF Frequency) Calibration Planes If the mixer that you want to test is reciprocal, the result from the previous section is sufficient. However, if your mixer is not reciprocal (for example, it has an embedded amplifier), then it can still be measured in a two step process. Step 1 is to characterize a calibration mixer that is reciprocal, and Step 2 is use the characterized mixer to calibrate a VNA system, with an additional converter, that will allow measurements of any mixer. The calibration mixer still requires the image filter, but an additional filter may be part of the of the reconverting hardware interface chassis, such that the mixer under test need not have an image filter. Normal VNA calibration techniques can be used to ascertain the error terms of Port 1 and the load match of the interface chassis.

Step Two: Measure the uncorrected response of the cal mixer, S21M1
Place calibration mixer in path, and measure S21M1 Calculate ETF from the known mixer terms, error terms, and S21M1 The transmission tracking term must be created for the calibration from the measurements of the characterized calibration mixer. This slide shows the signal flow graph, from which the equation for the Forward Transmission tracking term may be calculated.

Download cal terms and turn on 2-port cal
During calibration ETF is corrected for source match, mixer input match, mixer output match, and load match. Also ERF, ESF, EDF and ELF were calculated at the VNA ports. ELR, ESR, EDR terms are set to 0 and ETR and ERR are set to 1 since S12 and S22 are not measured. Provides an input-match-corrected transmission and reflection measurement. Mixer output-match and reverse-transmission not measured. Allows real time vector measurements of mixer. These error terms are gathered together in one cal set, and downloaded into the VNA. Because the measurement system cannot measure S12 and S22 directly, the reverse error terms are set to zero or one, so their effect on the correction computation is removed. This modified 2-port calibration does an input-match-corrected transmission and reflection measurement. Since the characterized mixer is characterized in magnitude and phase, any other mixer may also be characterized in magnitude and phase. This system does not have the limitations of measuring a reciprocal mixer, but does have the limitation that the LO drives be the same for up and down conversion.

Comparison Measurement: Mixer+Airline
Mixer with Airline and vector cal: Gray Trace Mixer with Airline, normalization: Blue Trace This measurement shows the response between two measurements of the same mixer, with two different calibration techniques. In each case, the conversion loss is measured, and normalized, then an nearly ideal transmission line (also known as an airline) is added and the combination re-measured. The gray trace shows the result with a vector calibration, as previously described. The blue trace shows the result using a scalar calibration, which does not correct for input mismatch. The improvement due to vector calibration is obvious.

Calibration Mixer Characterization: Amplitude Compared with Power Meter Measurements
Mixer Measured as up and down converter, using power meter measurements. Black trace is the average of up/down conversion Mixer Measured as up and down converter, using the new method The final question to be answered is: how good is the assumption that the mixer is reciprocal? Here, the mixer was tested as both an up and down converter, over the same frequency range using filtered power meter measurements (left hand plot). The black line is the average of the up/down measurement. The difference between the average and the up or down measurement is the error. Worst case is less than 0.2 dB. This can be converted to predict a phase error of less than 1.2 degrees. The right hand plot shows the characterization technique applied to the mixer first as an up converter, then as a down converter. There is virtually no difference between these measurements, and they match almost exactly the average (black trace) of the power meter based measurements. This indicates that we can characterize the calibration mixer either as an up or down converter (whichever is more convenient for filtering) and it will be valid used in the other direction. The fact that the power meter average is identical to the new method indicates our analysis that ERF=S21*S12 is valid.

Calibration Mixer Characterization: Phase response and Group Delay
Phase Response of Mixer, (Measured as up and down converter) Group Delay Response of Mixer, (Measured as up and down converter) Finally, the most import plot, shows the phase of the calibration mixer characterized as an up and a down converter. Again, there is virtually no difference. The right hand plot shows the absolute group delay of the calibration mixer (including it’s image filter), and has remarkably little noise or ripple on the measurement. Depending on delay aperture, group delay resolution less than 100 ps on mixer measurements is easily obtained.

Comparison Mixer Measurements
Characterization of calibration mixer Mixer comparison network analyzer Test Path Ref Path or Golden-Mixer Test-Mixer After Cal Another way to measure mixers is to compare a “golden-mixer” to the test-mixer connected in the test path. The reference mixer is placed in the reference path to provide a frequency conversion to match the frequency conversion caused by the test mixer in the test path. This method provides the same test frequency for both the reference and test paths and allows for comparison amplitude and phase measurements. The reference mixer is just for synchronization purpose and the actual comparison is between the “golden-mixer” and the test-mixer in the test path. This method can be improved by using a characterized calibration mixer in place of the “golden-mixer.” The network analyzer can then be calibrated to make error corrected magnitude and phase measurements of the test mixer. The reverse transmission path of the test-mixer can not be measured with this block diagram which introduces a fairly small uncertainty in the error corrected results. In the error correction this is done by setting ELR (load match in reverse direction) to zero. The characterization of the calibration mixer is done using the same technique described earlier.

Comparison Mixer Measurements
This is the complete block diagram of the mixer test set. There is a port available to connect the reference mixer. And ports to add attenuators and amplifiers for high power measurements.

Complete Mixer Characterization
Int Source Int LO Meas S11 RF b0/a0 S21 IF b3/aR S12 b0/aR S22 b3/a3 This block diagram describes a system for complete characterization of the forward and reverse paths of a test-mixer. All four s-parameters of the test-mixer can be measured with no assumptions. Calibration can be done using the characterized calibration mixer described earlier. Or this block diagram can support the unknown thru calibration technique using a reciprocal mixer as the unknown thru calibration element. However there can be remaining errors due to the image and various higher order mixing products. These errors may vary as the RF, IF and LO port matches reflect these higher order products back into the mixer and remix to the primary operating frequencies.

Summary Common mixer measurement techniques lack the ability to accurately measure phase or delay of mixers. A new technique, based on reflection measurements, resolves this problem, and provides accurate and repeatable measurements of reciprocal mixers for both magnitude and phase response. Mixers characterized in this way can be used to calibrate test systems, such that non-reciprocal mixers can be measured for phase and absolute delay. Comparison mixer characterization was described. Complete mixer characterization approach was proposed.

Consider “Hi-side” LO mixers For image mixers note the frequency sweep reversal, which implies phase conjugation

Mixer Characterization for an Image Mixer: Very poor result for extracted S22, but only when use characterized (Ecal) devices (not mechanical standards) S22 from VNA S22 from Mixer char.

Image Mixer Definition of Waves

New Rule for Image Mixers
aLO aIF bIF aIM bIM SIF* SIF

Take the Conjugate of the Load Simple rules for dealing with moving a reflection from the output of an image mixer to its input

S21 Characterization With and without an added airline and with and without using the conjugate of the load

S22 Characterization Shows the proper response when extracted with the conjugate load technique
IM IF Precision Match

Image Mixer Summary Common mixer measurement techniques lack the ability to accurately measure phase or delay of mixers A previous technique based on reflection measurements resolves this problem, and provides accurate and repeatable measurements of reciprocal mixers for both magnitude and phase response, but fails to give the correct response for “image” mixers. That technique is modified to account for the phase reversal of image mixers, namely by using the conjugate of the reflection loads. A theory of image mixer conversion parameters has been introduced, which predict and account for the phase-reversal effects. Several measurements verify the new technique, and underlying theory

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