Heng Chan; Mohawk College

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Heng Chan; Mohawk College
Communications 2 EE555 Heng Chan; Mohawk College

Heng Chan; Mohawk College
Course Content Introduction & Review Transmission Line Characteristics Waveguides & Microwave Devices Radiowave Propagation Antennas Microwave Radio & Radar Systems Fibre Optic Communications Heng Chan; Mohawk College

Heng Chan; Mohawk College
Introduction & Review Microwaves are defined as radio waves in the frequency range > 1 GHz. However, waves > 20 GHz are commonly known as millimeter waves Distributed, rather than lumped, circuit elements must be used at microwave frequencies because of a phenomenon called skin effect. Heng Chan; Mohawk College

Heng Chan; Mohawk College
Skin Effect At microwave frequencies current travels on the outer surface, or skin, of the conductor because of the increased inductance created. The skin depth ,  (in m), for a conductor with permeability,  (in H/m), conductivity,  (in S/m), and at a frequency, f (in Hz), is given by: Heng Chan; Mohawk College

Heng Chan; Mohawk College
Skin Effect (cont’d) J The current density, J, decreases with the distance beneath the surface exponentially. At a depth , the current density decreases to Jo/e. As f increases,   and resistance . Jo J = Joe-z/d z conductor surface direction of current Heng Chan; Mohawk College

Transverse Electromagnetic Waves
In free space: z Direction of Propagation y Magnetic Field Electric Field x Heng Chan; Mohawk College

Heng Chan; Mohawk College
Notes on TEM Waves The E- and H-fields and the direction of motion of TEM waves are mutually perpendicular to each other. Velocity of radio waves in free space is c = 3x108 m/s, but in a medium with dielectric constant r: Heng Chan; Mohawk College

Heng Chan; Mohawk College
Microwave Materials Glass epoxy printed circuit boards are unsuitable for microwave use because of high dissipation factor and wide tolerance in thickness and dielectric constant. Instead, materials such as Teflon fiberglass laminates, alumina substrates, sapphire and quartz substrates must be used (refer to text for details). Heng Chan; Mohawk College

Types of Transmission Lines
Differential or balanced lines (where neither conductor is grounded): e.g. twin lead, twisted-cable pair, and shielded-cable pair. Single-ended or unbalanced lines (where one conductor is grounded): e.g. concentric or coaxial cable. Transmission lines for microwave use: e.g. striplines, microstrips, and waveguides. Heng Chan; Mohawk College

Transmission Line Equivalent Circuit
Zo Zo C G C C C G “Lossy” Line Lossless Line Heng Chan; Mohawk College

Notes on Transmission Line
Characteristics of a line is determined by its primary electrical constants or distributed parameters: R (/m), L (H/m), C (F/m), and G (S/m). Characteristic impedance, Zo, is defined as the input impedance of an infinite line or that of a finite line terminated with a load impedance, ZL = Zo. Heng Chan; Mohawk College

Formulas for Some Lines
For parallel two-wire line: D d m = momr; e = eoer; mo = 4px10-7 H/m; eo = pF/m For co-axial cable: D d Heng Chan; Mohawk College

Transmission-Line Wave Propagation
Electromagnetic waves travel at < c in a transmission line because of the dielectric separating the conductors. The velocity of propagation is given by: m/s Velocity factor, VF, is defined as: Heng Chan; Mohawk College

Heng Chan; Mohawk College
Propagation Constant Propagation constant, , determines the variation of V or I with distance along the line: V = Vse-x; I = Ise-x, where VS, and IS are the voltage and current at the source end, and x = distance from source.  =  + j, where  = attenuation coefficient (= 0 for lossless line), and  = phase shift coefficient = 2/ (rad./m) Heng Chan; Mohawk College

Incident & Reflected Waves
For an infinitely long line or a line terminated with a matched load, no incident power is reflected. The line is called a flat or nonresonant line. For a finite line with no matching termination, part or all of the incident voltage and current will be reflected. Heng Chan; Mohawk College

Reflection Coefficient
The reflection coefficient is defined as: It can also be shown that: Note that when ZL = Zo,  = 0; when ZL = 0,  = -1; and when ZL = open circuit,  = 1. Heng Chan; Mohawk College

Heng Chan; Mohawk College
Standing Waves Voltage Vmax = Ei + Er Vmin = Ei - Er l 2 With a mismatched line, the incident and reflected waves set up an interference pattern on the line known as a standing wave. The standing wave ratio is : Heng Chan; Mohawk College

Heng Chan; Mohawk College
Other Formulas When the load is purely resistive: (whichever gives an SWR > 1) Return Loss, RL = Fraction of power reflected = ||2, or -20 log || dB So, Pr = ||2Pi Mismatched Loss, ML = Fraction of power transmitted/absorbed = 1 - ||2 or -10 log(1-||2) dB So, Pt = Pi (1 - ||2) = Pi - Pr Heng Chan; Mohawk College

Time-Domain Reflectometry
ZL Transmission Line Oscilloscope Pulse or Step Generator TDR is a practical technique for determining the length of the line, the way it is terminated, and the type and location of any impedance discontinuities. The distance to the discontinuity is: d = vt/2, where t = elapsed time of returned reflection. Heng Chan; Mohawk College

Typical TDR Waveform Displays
Vr Vi Vr t Vi RL > Zo RL < Zo ZL inductive ZL capacitive Heng Chan; Mohawk College

Transmission-Line Input Impedance
The input impedance at a distance l from the load is: When the load is a short circuit, Zi = jZo tan (l). For 0  l < /4, shorted line is inductive. For l = /4, shorted line = a parallel resonant circuit. For /4 < l  /2, shorted line is capacitive. Heng Chan; Mohawk College

T-L Input Impedance (cont’d)
When the load is an open circuit, Zi = -jZo cot (l) For 0 < l < /4, open circuited line is capacitive. For l = /4, open-line = series resonant circuit. For /4 < l < /2, open-line is inductive. A /4 line with characteristic impedance, Zo’, can be used as a matching transformer between a resistive load, ZL, and a line with characteristic impedance, Zo, by choosing: Heng Chan; Mohawk College

Transmission Line Summary
or is equivalent to: l < /4 l > /4 or is equivalent to: l > /4 l < /4 /4 = Zo ZL Zo’ l = /4 /4-section Matching Transformer = Heng Chan; Mohawk College

Heng Chan; Mohawk College
The Smith Chart The Smith chart is a graphical aid to solving transmission-line impedance problems. The coordinates on the chart are based on the intersection of two sets of orthogonal circles. One set represents the normalized resistive component, r (= R/Zo), and the other the normalized reactive component, ± jx (= ± jX/Zo). Heng Chan; Mohawk College

Heng Chan; Mohawk College
Smith Chart Basics +j0.7 r = 0 z1 z1 = 1+j0.7 r = 2 j0 z2 r = 1 z2 = 2-j1.4 -j1.4 Heng Chan; Mohawk College

Applications of The Smith Chart
Applications to be discussed in this course: Find SWR, ||, RL Find YL Find Zi of a shorted or open line of length l Find Zi of a line terminated with ZL Find distance to Vmax and Vmin from ZL Solution for quarter-wave transformer matching Solution for parallel single-stub matching Heng Chan; Mohawk College

Heng Chan; Mohawk College
Substrate Lines Miniaturized microwave circuits use striplines and microstrips rather than coaxial cables as transmission lines for greater flexibility and compactness in design. The basic stripline structure consists of a flat conductor embedded in a dielectric material and sandwiched between two ground planes. Heng Chan; Mohawk College

Basic Stripline Structure
Ground Planes W b t er Solid Dielectric Centre Conductor Heng Chan; Mohawk College

Heng Chan; Mohawk College
Notes On Striplines When properly designed, the E and H fields of the signal are completely confined within the dielectric material between the two ground planes. The characteristic impedance of the stripline is a function of its line geometry, specifically, the t/b and w/b ratios, and the dielectric constant, r. Graphs, design formulas, or computer programs are available to determine w for a desired Zo, t, and b. Heng Chan; Mohawk College

Heng Chan; Mohawk College
Microstrip w Circuit Line t r (dielectric) b Ground Plane Microstrip line employs a single ground plane, the conductor pattern on the top surface being open. Graphs, formulas or computer programs would be used to design the conductor line width. However, since the electromagnetic field is partly in the solid dielectric, and partly in the air space, the effective relative permittivity, eff, has to be used in the design instead of r. Heng Chan; Mohawk College

Stripline vs Microstrip
Advantages of stripline: signal is shielded from external interference shielding prevents radiation loss r and mode of propagation are more predictable for design Advantages of microstrip: easier to fabricate, therefore less costly easier to lay, repair/replace components Heng Chan; Mohawk College

Microstrip Directional Coupler
2 4 Conductor Lines /4 Dielectric Ground Plane Top View Cross-sectional View 1 3 Most of the power into port #1 will flow to port #3. Some of the power will be coupled to port #2 but only a minute amount will go to port #4. Heng Chan; Mohawk College

Formulas For Directional Coupler
The operation of the coupler gives rise to an even mode characteristic impedance, Zoe, and an odd mode characteristic impedance, Zoo, where: For a given coupling factor, C (which is V2/V1): Heng Chan; Mohawk College

Heng Chan; Mohawk College
Coupler Applications Some common applications for couplers: monitoring/measuring the power or frequency at a point in the circuit sampling the microwave energy for used in automatic leveling circuits (ALC) reflection measurements which indirectly yield information on VSWR, ZL, return loss, etc. Heng Chan; Mohawk College

Heng Chan; Mohawk College
Branch Coupler Z1 = Zo Input power at port #1 will divide equally between Ports 2 and 3 and none to port 4. l/4 4 3 Z1 l/4 Zo Zo Z1 2 1 Can provide tighter coupling and can handle higher power than directional coupler. Branches may consist of chokes, filters, or matched load for more design flexibility. Heng Chan; Mohawk College

Heng Chan; Mohawk College
Hybrid Ring Coupler Input power at port #1 divides evenly between ports 2 & 4 and none for port 3. 3l/4 4 1 l/4 l/4 Similarly, input at port #2 will divide evenly between ports 1 and 3 and none for port 4. l/4 3 2 One application: circulator. Heng Chan; Mohawk College

Microstrip & Stripline Filters
/4 OUT Side-coupled half-wave resonator band-pass filter IN L L L L OUT C C C Conventional low-pass filter Heng Chan; Mohawk College

Scattering Parameters
Microwave devices are often characterized by their S-parameters because: measurement of V and I may be difficult at microwave frequencies. Active devices frequently become unstable when open or short-circuit type measurements are made for h, Y or Z parameters. An [S] matrix is used to contain all the S-parameters. Heng Chan; Mohawk College

S-Variables & S-Parameters
2-Port Network V1 V2 b1 b2 For port x: Vx = Vix + Vrx ; S-variables: Px = Pix - Prx = |ax|2-|bx|2 b1 = S11a1 + S12a2 b2 = S21a1 + S22a2 or Heng Chan; Mohawk College

S-Parameters of 2-Port Network
Note: when port 2 is terminated with a matched load, a2 = 0. Similarly, a1 = 0 when port 1 is matched. S11, and S22 are reflection coefficients, i.e., 11, & 22. S21 represents the forward transmission coefficient. Thus, Insertion Loss/attenuation = -10 log (Po2/Pi1) = -20 log |S21| dB S12 is the reversed transmission coefficient. Heng Chan; Mohawk College

Properties of S-Parameters
In general, S-parameters have both magnitude and angle. For matched 2-port reflectionless networks, S11 = S22 = 0 For a reciprocal 2-port network, S12 = S21. For a lossless 2-port network, S12 = S21 = 1. For n-port, [b] = [S] [a]. The n x n [S] matrix characterizes the network. Heng Chan; Mohawk College

The fact that microwaves can be used for cooking purposes and in heating applications suggests that they have the potential for causing biological damage. Health & Welfare, Canada specifies no limit exposure duration for radiation level of 1 mW/cm2 or less for frequencies from 10 MHz to 300 GHz. Avoid being in the direct path of a microwave beam coming out of an antenna or waveguide. Heng Chan; Mohawk College

Heng Chan; Mohawk College
Waveguides Reasons for using waveguide rather than coaxial cable at microwave frequency: easier to fabricate no solid dielectric and I2R losses Waveguides do not support TEM waves inside because of boundary conditions. Waves travel zig-zag down the waveguide by bouncing from one side wall to the other. Heng Chan; Mohawk College

E-Field Pattern of TE1 0 Mode
b a g/2 End View Side View TEmn means there are m number of half-wave variations of the transverse E-field along the “a” side and n number of half-wave variations along the “b” side. The magnetic field (not shown) forms closed loops horizontally around the E-field Heng Chan; Mohawk College

Heng Chan; Mohawk College
TE and TM Modes TEmn mode has the E-field entirely transverse, i.e. perpendicular, to the direction of propagation. TMmn mode has the H-field entirely transverse to the direction of propagation. All TEmn and TMmn modes are theoretically permissible except, in a rectangular waveguide, TMmo or TMon modes are not possible since the magnetic field must form a closed loop. In practice, only the dominant mode, TE10 is used. Heng Chan; Mohawk College

Wavelength for TE & TM Modes
Cutoff wavelength: Any signal with l  lc will not propagate down the waveguide. For air-filled waveguide, cutoff freq., fc = c/lc TE10 is called the dominant mode since lc = 2a is the longest wavelength of any mode. Guide wavelength: Heng Chan; Mohawk College

Other Formulas for TE & TM Modes
Group velocity: Phase velocity: Wave impedance: Zo = 377 W for air-filled waveguide Heng Chan; Mohawk College

Circular/Cylindrical Waveguides
Differences versus rectangular waveguides : lc = 2pr/Bmn where r = waveguide radius, and Bmn is obtained from table of Bessel functions. All TEmn and TMmn modes are supported since m and n subscripts are defined differently. Dominant mode is TE11. Advantages: higher power-handling capacity, lower attenuation for a given cutoff wavelength. Disadvantages: larger and heavier. Heng Chan; Mohawk College

Waveguide Terminations
lg/2 Dissipative Vane Short-circuit Sliding Short-Circuit Side View End View Dissipative vane is coated with a thin film of metal which in turn has a thin dielectric coating for protection. Its impedance is made equal to the wave impedance. The taper minimizes reflection. Sliding short-circuit functions like a shorted stub for impedance matching purpose. Heng Chan; Mohawk College

Heng Chan; Mohawk College
Attenuators Resistive Flap Max. attenuation when flap is fully inside. Slot for flap is chosen to be at a non- radiating position. Pi Po Rotary-vane Type Atten.(dB) = 10 log (Pi/Po) = -20 log |S21| Max. attenuation when vane is at centre of guide and min. at the side-wall. Pi Po Sliding-vane Type Heng Chan; Mohawk College

Heng Chan; Mohawk College
Iris Reactors Inductive iris; vanes are vertical = Capacitive iris; vanes are horizontal = Irises can be used as reactance elements, filters or impedance matching devices. = Heng Chan; Mohawk College

Heng Chan; Mohawk College
Tuning Screw s Tuning Screws Post A post or screw can also serve as a reactive element. When the screw is advanced partway into the wave- guide, it acts capacitive. When the screw is advanced all the way into the waveguide, it acts inductive. In between the two positions, one can get a resonant LC circuit. Heng Chan; Mohawk College

Waveguide T-Junctions
2 3 3 1 2 1 E-Plane Junction H-Plane Junction Input power at port 2 will split equally between ports 1 and 3 but the outputs will be antiphase for E-plane T and inphase for H-plane T. Input power at ports 1 & 3 will combine and exit from port 1 provided the correct phasing is used. Heng Chan; Mohawk College

S-Matrix for T-Junctions
For ideal T-junction: Note: + sign is used for H-plane T, and (-) sign for E-plane T. Also note that even though S22 = 0 (i.e. “lossless”), S11 and S33 are each equal to 1/2, i.e., input power applied to ports 1 and 3 will always suffer from reflection. Heng Chan; Mohawk College

Heng Chan; Mohawk College
Hybrid-T Junction 3 Under matched & ideal conditions: 2 1 4 It combines E-plane and H-plane junctions. Note : S11, S22, S33, and S44 are zero. Pin at port 1 or 2 will divide between ports 3 and 4. Pin at port 3 or 4 will divide between ports 1 and 2. Heng Chan; Mohawk College

Hybrid-T Junction (cont’d)
If input power of the same phase is applied simultaneously at ports 1 and 2, the combined power exits from port 4. If the input is out-of-phase, the output is at port 3. Applications: Combining power from two transmitters. TX and a RX sharing a common antenna. Low noise mixer circuit. Heng Chan; Mohawk College

Heng Chan; Mohawk College
Directional Coupler lg/4 P4 Termination P3 P1 P2 P1 P2 2-hole Coupler Holes spaced lg/4 allow waves travelling toward port 4 to combine. Waves travelling toward port 3, however, will cancel. Therefore, ideally P3 = 0. To broaden frequency response bandwidth, practical couplers would usually have multi holes. Heng Chan; Mohawk College

Directional Coupler (cont’d)
For ideal directional coupler: where a2 + b2 = 1 Definitions: Coupling Factor, Directivity, Insertion Loss (dB) = 10 log (P1/P2) = -20 log |S12| Heng Chan; Mohawk College

Heng Chan; Mohawk College
Cavity Resonators Resonant wavelength for a rectangular cavity: b L a For a cylindrical resonator: r L Heng Chan; Mohawk College

Cavity Resonators (cont’d)
Energy is coupled into the cavity either through a small opening, by a coupling loop or a coupling probe. These methods of coupling also apply for waveguides Applications of resonators: filters absorption wavemeters microwave tubes Heng Chan; Mohawk College

Heng Chan; Mohawk College
Ferrite Components Ferrites are compounds of metallic oxides such as those of Fe, Zn, Mn, Mg, Co, Al, and Ni. They have magnetic properties similar to ferromagnetic metals and at the same time have high resistivity associated with dielectrics. Their magnetic properties can be controlled by means of an external magnetic field. They can be transparent, reflective, absorptive, or cause wave rotation depending on the H-field.. Heng Chan; Mohawk College

Examples of Ferrite Devices
Isolator Attenuator 2 q 1 3 Differential Phase Shifter 4-port Circulator 4 Heng Chan; Mohawk College

Notes On Ferrite Devices
Differential phase shifter - q is the phase shift between the two directions of propagation. Isolator - permits power flow in one direction only. Circulator - power entering port 1 will go to port 2 only; power entering port 2 will go to port 3 only; etc. Most of the above are based on Faraday rotation. Other usage: filters, resonators, and substrates. Heng Chan; Mohawk College

Schottky Barrier Diode
Metal Electrode Contact It’s based on a simple metal- semiconductor interface. There is no p-n junction but a depletion region exists. Current is by majority carriers; therefore, very low in capacitance. Semi- conductor Layer SiO2 Dielectric Substrate Metal Electrode Applications: detectors, mixers, and switches. Heng Chan; Mohawk College

Varactor Diode Varactors operate under reverse-bias conditions.
Cj Co Circuit Symbol V Junction Capacitance Characteristic Varactors operate under reverse-bias conditions. The junction capacitance is: where Vb = barrier potential (0.55 to 0.7 for silicon) and K = constant (often = 1) Heng Chan; Mohawk College

Equivalent Circuit for Varactor
The series resistance, Rs, and diode capacitance, Cj, determine the cutoff frequency: Cj Rj Rs The diode quality factor for a given frequency, f, is: Heng Chan; Mohawk College

Varactor Applications
Voltage-controlled oscillator (VCO) in AFC and PLL circuits Variable phase shifter Harmonic generator in frequency multiplier circuits Up or down converter circuits Parametric amplifier circuits - low noise Heng Chan; Mohawk College

Parametric Amplifier Circuit
Pump signal (fp) Degenerative Mode: fp = 2fs Nondegenerative mode: L2 Upconversion - fi = fs + fp Downconversion - fi = fs - fp Power gain, G = fi /fs C2 C1 Input signal (fs) Regenerative mode: negative resistance very low noise very high gain fp = fs + fi C3 L1 D1 L3 Signal tank (fs) Idler tank (fi) Heng Chan; Mohawk College

Heng Chan; Mohawk College
PIN Diode S1 RFC R +V P+ C2 C1 I In Out N+ D1 PIN as shunt switch PIN diode has an intrinsic region between the P+ and N+ materials. It has a very high resistance in the OFF mode and a very low resistance when forward biased. Heng Chan; Mohawk College

PIN Diode Applications
To switch devices such as attenuators, filters, and amplifiers in and out of the circuit. Voltage-variable attenuator Amplitude modulator Transmit-receive (TR) switch Phase shifter (with section of transmission line) Heng Chan; Mohawk College

Heng Chan; Mohawk College
Tunnel Diode i Ls Ip Cj -R A B C Rs V Symbol Equivalent Circuit Vp Vv Characteristic Curve Heavy doping of the semiconductor material creates a very thin potential barrier in the depletion zone which leads to electron tunneling through the barrier. Note the negative resistance zone between Vp and Vv. Heng Chan; Mohawk College

More Notes On Tunnel Diode
Tunnel diodes can be used in monostable (A or C), bistable (between A and C), or astable (B) modes. These modes lead to switching, oscillation, and amplification applications. However, the power output levels of the tunnel diode are restricted to a few mW only. The resistive, and self-resonant frequencies are: Heng Chan; Mohawk College

Transferred Electron Devices
TEDs are made of compound semiconductors such as GaAs. They exhibit periodic fluctuations of current due to negative resistance effects when a threshold voltage (about 3.4 V) is exceeded. The negative resistance effect is due to electrons being swept from a lower valley (more mobile) region to an upper valley (less mobile) region in the conduction band. Heng Chan; Mohawk College

Heng Chan; Mohawk College
Gunn Diode The Gunn diode is a transferred electron device that can be used in microwave oscillators or one-port reflection amplifiers. Its basic structure is shown below. N-, the active region, is sandwiched between two heavily doped N+ regions. Electrons from the l cathode (K) drifts to the anode (A) in bunched formation called domains. Note that there is no p-n junction. K N- A Metallic Electrode N+ Metallic Electrode Heng Chan; Mohawk College

Heng Chan; Mohawk College
Gunn Operating Modes Stable Amplification (SA) Mode: diode behaves as an amplifier due to negative resistance effect. Transit Time (TT) Mode: operating frequency, fo = vd / l where vd is the domain velocity, and l is the effective length. Output power < 2 W, and frequency is between 1 GHz to 18 GHz. Limited Space-Charge (LSA) Mode: requires a high-Q resonant cavity; operating frequency up to 100 GHz and pulsed output power > 100 W. Heng Chan; Mohawk College

Gunn Diode Circuit and Applications
Resonant Cavity Tuning Screw The resonant cavity is shocked excited by current pulses from the Gunn diode and the RF energy is coupled via the iris to the waveguide. Iris Diode V Gunn diode applications: microwave source for receiver local oscillator, police radars, and microwave communication links. Heng Chan; Mohawk College

Avalanche Transit-Time Devices
If the reverse-bias potential exceeds a certain threshold, the diode breaks down. Energetic carriers collide with bound electrons to create more hole-electron pairs. This multiplies to cause a rapid increase in reverse current. The onset of avalanche current and its drift across the diode is out of phase with the applied voltage thus producing a negative resistance phenomenon. Heng Chan; Mohawk College

Heng Chan; Mohawk College
IMPATT Diode A single-drift structure of an IMPATT (impact avalanche transit time) diode is shown below: - + P+ N N+ l Avalanche Region Drift Region Operating frequency: where vd = drift velocity Heng Chan; Mohawk College

Heng Chan; Mohawk College
Notes On IMPATT Diode The current build-up and the transit time for the current pulse to cross the drift region cause a 180o phase delay between V and I; thus, negative R. IMPATT diodes typically operate in the 3 to 6 GHz region but higher frequencies are possible. They must operate in conjunction with an external high-Q resonant circuit. They have relatively high output power (>100 W pulsed) but are very noisy and not very efficient. Heng Chan; Mohawk College

Microwave Transistors
Silicon BJTs and GaAsFETs are most widely used. BJT useful for amplification up to about 6 MHz. MesFET (metal semiconductor FET) and HEMT (high electron mobility transistor) are operable beyond 60 GHz. FETs have higher input impedance, better efficiency and more frequency stable than BJTs. Heng Chan; Mohawk College

Microwave Transistor Power Gain
Zs Matching Network GL Matching Network Gs Transistor Go ZL Vs Max. power gain of a unilateral transistor amplifier with conjugate matched input and output: Note that Go = |S21|2 is the gain of the transistor. For unconditional stability, |S11| < 1 and |S22| < 1. Heng Chan; Mohawk College

Noise Factor & Noise Figure
Noise Factor, Fn = SNRin/SNRout Noise Figure, NF (dB) = 10 log Fn = SNRin (dB) - SNRout (dB) Equivalent noise temperature, Te = (Fn -1) To where To = 290 oK For amplifiers in cascade, the overall noise factor: where Gn = amplifier gain of the nth stage. Heng Chan; Mohawk College

Heng Chan; Mohawk College
Microwave Tubes Classical vacuum tubes have several factors which limit their upper operating frequency: interelectrode capacitance & lead inductance dielectric losses & skin effect transit time Microwave tubes utilize resonant cavities and the interaction between the electric field, magnetic field and the electrons. Heng Chan; Mohawk College

Heng Chan ; Mohawk College
Magnetrons It consists of a cylindrical cathode surrounded by the anode with a number of resonant cavities. It’s a crossed-field device since the E-field is perpendicular to the dc magnetic field. Interaction Space Waveguide Output At a critical voltage the electrons from the cathode will just graze the anode. Cavity Coupling Window Anode Cathode Heng Chan ; Mohawk College

Heng Chan; Mohawk College
Magnetron Operation When an electron cloud sweeps past a cavity, it excites the latter to self oscillation which in turn causes the electrons to bunch up into a spoked wheel formation in the interaction space. The continuous exchange of energy between the electrons and the cavities sustains oscillations at microwave frequency. Electrons will eventually lose their energy and fall back into the cathode while new ones are emitted. Heng Chan; Mohawk College

More Notes On Magnetrons
Alternate cavities are strapped (i.e., shorted) so that adjacent resonators are 180o out of phase. This enables only the dominant p-mode to operate. Frequency tuning is possible either mechanically (screw tuner) or electrically with voltage. Magnetrons are used as oscillators for radars, beacons, microwave ovens, etc. Peak output power is from a few MW at UHF and X-band to 10 kW at 100 GHz. Heng Chan; Mohawk College

Heng Chan; Mohawk College
Klystrons Klystrons are linear-beam devices since the E-field is parallel to the static magnetic field. Their operation is based on velocity and density modulation with resonating cavities to create the bunching effect. They can be employed as oscillators or power amplifiers. Heng Chan; Mohawk College

Two-Cavity Klystron v Effect of velocity modulation RF In RF Out
Control Grid Gap Filament Collector Cathode Drift Region Buncher Cavity Catcher Cavity Anode v Electron Beam Effect of velocity modulation Heng Chan; Mohawk College

Heng Chan; Mohawk College
Klystron Operation RF signal applied to the buncher cavity sets up an alternating field across the buncher gap. This field alternately accelerates and decelerates the electron beam causing electrons to bunch up in the drift region. When the electron bundles pass the catcher gap, they excite the catcher cavity into resonance. RF power is extracted from the catcher cavity by the coupling loop. Heng Chan; Mohawk College

Multicavity Klystrons
Gain can be increased by inserting intermediate cavities between the buncher and catcher cavity. Each additional cavity increases power gain by 15- to 20-dB. Synchronous tuned klystrons have high gain but very narrow bandwidth, e.g % of fo. Stagger tuned klystrons have wider bandwidth at the expense of gain. Can operate as oscillator by positive feedback. Heng Chan; Mohawk College

Heng Chan; Mohawk College
Reflex Klystron Output Anode Cavity Cathode Repeller Filament Electron Beam Vr Condition for oscillation requires electron transit time to be: where n = an integer and T = period of oscillation Heng Chan; Mohawk College

Reflex Klystron Operation
Electron beam is velocity modulated when passing though gridded gap of the cavity. Repeller decelerates and turns back electrons thus causing bunching. Electrons are collected on the cavity walls and output power can be extracted. Repeller voltage, Vr, can be used to vary output frequency and power. Heng Chan; Mohawk College

Notes On Reflex Klystrons
Only one cavity used. No external dc magnetic field required. Compact size. Can be used as an oscillator only. Low output power and low efficiency. Output frequency can be tuned by Vr , or by changing the dimensions of the cavity. Heng Chan; Mohawk College

Heng Chan; Mohawk College
Travelling-Wave Tube RF In RF Out Helix Collector Electron Beam Attenuator The TWT is a linear beam device with the magnetic field running parallel to tube lengthwise. The helix is also known as a slow wave structure to slow down the RF field so that its velocity down the the tube is close to the velocity of the electron beam. Heng Chan; Mohawk College

Heng Chan; Mohawk College
TWT Operation As the RF wave travels along the helix, its positive and negative oscillations velocity modulate the electron beam causing the electrons to bunch up. The prolonged interaction between the RF wave and electron beam along the TWT results in exponential growth of the RF voltage. The amplified wave is then extracted at the output. The attenuator prevents reflected waves that can cause oscillations. Heng Chan; Mohawk College

Heng Chan; Mohawk College
Notes On TWTs Since interaction between the RF field and the electron beam is over the entire length of the tube, the power gain achievable is very high (> 50 dB). As TWTs are nonresonant devices, they have wider bandwidths and lower NF than klystrons. TWTs operate from 0.3 to 50 GHz. The Twystron tube is a combination of the TWT and klystron. It gives better gain and BW over either the conventional TWT or klystron. Heng Chan; Mohawk College

Radio- Wave In Free Space
Radio waves propagate as TEM waves in free space. For an isotropic (i.e. omnidirectional) source: d Point Source where PD = power density (W/m2); E = electric field intensity (V/m); Pr = total radiated power (W); and d = distance from source (m). Heng Chan; Mohawk College

Optical Properties Of Radio Waves
Since light waves and radio waves are part of the electromagnetic spectrum, they behave similarly. Thus, radio waves can: refract at the boundary between two different media reflect at the surface of a conductor diffract around the edge of an obstacle interfere with one and another to degrade performance Propagation of radio wave in the atmosphere is greatly influenced by the frequency of the wave. Heng Chan; Mohawk College

Radio Wave Propagation Modes
In every terrestrial radio system, there are three possible modes of propagation: Ground-wave or surface-wave propagation Space-wave or direct-wave propagation Sky-wave propagation At frequencies < 2 MHz, ground wave is best. Sky waves are used for HF signals. Space waves are used for VHF and above. Heng Chan; Mohawk College

Ground-Wave Propagation
Ground waves start out with the electric field being perpendicular to the ground. Due to the gradient density of the earth’s atmosphere the wavefront tilts progressively. Direction of wave travel Wavefront Increasing Tilt Earth Heng Chan; Mohawk College

Heng Chan; Mohawk College
Notes On Ground Waves Advantages: Given enough power, can circumnavigate the earth. Relatively unaffected by atmospheric conditions. Disadvantages: Require relatively high transmission power. Require large antennas since frequency is low. Ground losses vary considerably with terrain. Applications: MF broadcasting; ship-to-ship and ship-to-shore comms; radio navigation; maritime comms. Heng Chan; Mohawk College

Space-Wave Propagation
Most terrestrial communications in the VHF or higher frequency range use direct, line-of-sight, or tropospheric radio waves. The approximate maximum distance of communication is given by: where d = max. distance in km hT = height of the TX antenna in m hR = height of the RX antenna in m Heng Chan; Mohawk College

Heng Chan; Mohawk College
Notes On Space-Waves The radio horizon is greater than the optical horizon by about one third due to refraction of the atmosphere. Reflections from a relatively smooth surface, such as a body of water, could result in partial cancellation of the direct signal - a phenomenon known as fading. Also, large objects, such as buildings and hills, could cause multipath distortion from many reflections. Heng Chan; Mohawk College

Heng Chan; Mohawk College
Sky-Wave Propagation HF radio waves are returned from the F-layer of the ionosphere by a form of refraction. The highest frequency that is returned to earth in the vertical direction is called the critical frequency, fc. The highest frequency that returns to earth over a given path is called the maximum usable frequency (MUF). Because of the general instability of the ionosphere, the optimum working frequency (OWF) = 0.85 MUF, is used instead. Heng Chan; Mohawk College

Heng Chan; Mohawk College
Formulas For Sky Waves F-Layer From geometry (assuming flat earth): d = 2hv tan qi where hv = virtual height of F-layer From theory (secant law): MUF = fc sec qi qi hv Earth d Heng Chan; Mohawk College

Heng Chan; Mohawk College
Free-Space Path Loss Defined as the loss incurred by a radio wave as it travels in a straight line through a vacuum with no absorption or reflection of energy from nearby objects. Formula: Lp (dB) = log f + 20log d where f = frequency of radio wave in GHz and d = distance in km. If f is in MHz, replace 92.4 above by 32.4. Heng Chan; Mohawk College

Heng Chan; Mohawk College
Fade Margin To account for changes in atmospheric conditions, multipath loss, and terrain sensitivity, a fade margin, Fm, must be added to total system loss: Fm (dB) = 30log d + 10log(6ABf) - 10log(1-R) -70 where d = distance (km), f = frequency (GHz), R = reliability (decimal value), A = terrain roughness factor (0.25 to 4), and B = factor to convert worst-month probability to annual probability (0.125 to 1 depending on humidity or dryness). Heng Chan; Mohawk College

Heng Chan; Mohawk College
Antenna Basics An antenna is a passive reciprocal device. It acts as a transducer to convert electrical oscillations in a transmission line or waveguide to a propagating wave in free space and vice versa. It functions as an impedance matcher between a transmission line or waveguide and free space. All antennas have a radiation pattern which is a plot of the field strength or power density at various angular positions relative to the antenna. Heng Chan; Mohawk College

Heng Chan; Mohawk College
Antenna Efficiency An antenna has an equivalent radiation resistance, Rr given by: where Pr = power radiated and i = antenna current at feedpoint All the power supplied to the antenna is not radiated. Antenna efficiency: where Pd = power dissipated; and Re = effective antenna resistance. Heng Chan; Mohawk College

Directive Gain & Power Gain
Directive gain of an antenna is given by: where PD = power density at some point with a given antenna; PDr = power density at the same point with a reference antenna. Maximum directive gain is called directivity. Reference antenna is generally the isotropic source. When antenna efficiency is taken into account directive gain becomes power gain: Ap =  D. In decibels, power gain is 10 log Ap Heng Chan; Mohawk College

Effective Isotropic Radiated Power
EIRP is the equivalent power that an isotropic antenna would have to radiate to achieve the same power density at a given point as another antenna: EIRP = PrAt = PinAp where Pr = total radiated power; Pin = antenna input power; At = TX antenna directive gain; and Ap = antenna power gain. Therefore, the power density at a distance, d, from an antenna is: Heng Chan; Mohawk College

Heng Chan; Mohawk College
Antenna Miscellany Power captured by the receiving antenna with an effective area, Aeff, is C = PDAeff. Note that Aeff includes the gain and efficiency of the antenna. Antennas can be linearly, elliptically or circularly polarized depending on their E-field radiated. Antenna beamwidth is the angular separation between the two half-power points on the major lobe of the antenna’s plane radiation pattern. Antenna input impedance, Zin = Ei/Ii Heng Chan; Mohawk College

Heng Chan; Mohawk College
Half-Wave Dipole /2 Symbol Balanced Feedline Simple and most widely used at f > 2 MHz. It’s a resonant antenna since its length is 2 x l/4. Zin = 73 W approx.; Zmax = 2500 W approx. at ends Radiation pattern of dipole in free space has two main lobes perpendicular to the antenna axis. Has a gain of about 2.15 dBi Heng Chan; Mohawk College

Free-Space Radiation Pattern of Dipole
Heng Chan; Mohawk College

Ground & Length Effects On Dipole
Since the ground reflects radio waves, it has a significant effect on the radiation pattern and impedance of the half-wave dipole. Generally speaking, the closer the dipole is to the ground, the more lobes will form and the lower the radiation impedance. Length also has an effect on the dipole antenna: dipoles shorter than l/2 is capacitive while dipoles longer than l/2 is inductive. Heng Chan; Mohawk College

Marconi/Monopole Antenna
Main characteristics: vertical and l/4 good ground plane is required omnidirectional in the horizontal plane 3 dBd power gain impedance: about 36W Heng Chan; Mohawk College

Antenna Impedance Matching
Antennas should be matched to their feedline for maximum power transfer efficiency by using an LC matching network. A simple but effective technique for matching a short vertical antenna to a feedline is to increase its electrical length by adding an inductance at its base. This inductance, called a loading coil, cancels the capacitive effect of the antenna. Another method is to use capacitive loading. Heng Chan; Mohawk College

Heng Chan; Mohawk College

Heng Chan; Mohawk College
Antenna Arrays Antenna elements can be combined in an array to increase gain and get desired radiation pattern. Arrays can be classified as broadside or end-fire, according to their direction of maximum radiation. In a phased array, all elements are fed or driven; i.e. they are connected to the feedline. Some arrays have only one driven element with several parasitic elements which act to absorb and reradiate power radiated from the driven element. Heng Chan; Mohawk College

Heng Chan; Mohawk College
Yagi-Uda Array More commonly known as the Yagi array, it has one driven element, one reflector, and one or more directors. Radiation pattern Heng Chan; Mohawk College

Characteristics of Yagi Array
unidirectional radiation pattern (one main lobe, some sidelobes and backlobes) relatively narrow bandwidth since it is resonant 3-element array has a gain of about 7 dBi more directors will increase gain and reduce the beamwidth and feedpoint impedance a folded dipole is generally used for the driven element to widen the bandwidth and increase the feedpoint impedance. Heng Chan; Mohawk College

Heng Chan; Mohawk College
Folded Dipole Often used - alone or with other elements - for TV and FM broadcast receiving antennas because it has a wider bandwidth and four times the feedpoint resistance of a single dipole. l 2 Zin = 288 W Feed line Heng Chan; Mohawk College

Log-Periodic Dipole Array (LPDA)
Apex a L6 Feed line Direction of main lobe Heng Chan; Mohawk College

Characteristics of LPDA
feedpoint impedance is a periodic function of log f unidirectional radiation and wide bandwidth shortest element is less than or equal to l/2 of highest frequency, while longest element is at least l/2 of lowest frequency reasonable gain, but lower than that of Yagi for the same number of elements design parameter, t = L1/L2 = D1/D2 = L2/L3 = …. used mainly as HF, VHF, and TV antennas Heng Chan; Mohawk College

Heng Chan; Mohawk College
Turnstile Array Half-wave dipoles fed 90o out-of phase omnidirectional radiation in the horizontal plane, with horizontal polarization gain of about 3 dB less than that of a single dipole often used for FM broadcast RX and TX Heng Chan; Mohawk College

Heng Chan; Mohawk College
Collinear Array all elements lie along a straight line, fed in phase, and often mounted with main axis vertical result in narrow radiation beam omnidirectional in the horizontal plane when antenna is vertical Half-wave Elements Feed Line Quarter-wave Shorted Stub Heng Chan; Mohawk College

Heng Chan; Mohawk College
Broadside Array all l/2 elements are fed in phase and spaced l/2 with axis placed vertically, radiation would have a narrow bidirectional horizontal pattern Half-wave Dipoles Feed Line l 2 Heng Chan; Mohawk College

Heng Chan; Mohawk College
End-Fire Array dipole elements are fed 90o out of phase resulting in a narrow unidirectional radiation pattern off the end of the antenna Feed Line l 4 Half-wave Dipoles RadiationPattern Heng Chan; Mohawk College

Non-resonant Antennas
Monopole and dipole antennas are classified as resonant type since they operate efficiently only at frequencies that make their elements close to l/2. Non-resonant antennas do not use dipoles and are usually terminated with a matching load resistor. They have a broader bandwidth and a radiation pattern that has only one or two main lobes. Examples of non-resonant antennas are long-wire antennas, vee antennas, and rhombic antennas. Heng Chan; Mohawk College

Heng Chan; Mohawk College
Loop Antenna Main characteristics: very small dimensions bidirectional greatest sensitivity in the plane of the loop very wide bandwidth efficient as RX antenna with single or multi-turn loop Feedline Heng Chan; Mohawk College

Heng Chan; Mohawk College
Helical Antenna D broadband (+ 20% of fo) circularly polarized Ap= 15 dB; q-3dB = 20o are typical when S, D, & # of turns increase: Ap increases and q decreases to get higher gain and narrower beamwidth, use an array applications: V/UHF antenna; satellite tracking antenna S Ground Plane Coaxial Feedline End-fire Helical Antenna Heng Chan; Mohawk College

UHF & Microwave Antennas
highly directive and beamwidth of about 1o or less antenna dimensions >> wavelength of signal front-to-back ratio of 20 dB or more utilize parabolic reflector as secondary antenna for high gain primary feed is either a dipole or horn antenna use for point-to-point and satellite communications Heng Chan; Mohawk College

Parabolic Reflector Antenna
Power gain and -3 dB beamwidth are: where h = antenna efficiency (0.55 is typical); D = dish diameter (m); and l = wavelength (m) Heng Chan; Mohawk College

Heng Chan; Mohawk College
Hog-horn Antenna The hog-horn antenna, often used for terrestrial microwave links, integrates the feed horn and a parabolic reflecting surface to provide an obstruction-free path for incoming and outgoing signals. Parabolic Section Feed Horn Heng Chan; Mohawk College

Can be classified as either terrestrial or satellite systems. Early systems use FDM (frequency division multiplex) technique. More recent systems use PCM/PSK (pulse code modulation/phase shift keying) technique. Microwave system capacities range from less than 12 VB (voice-band) channels to > 22,000. Operate from 24 km to 6,400 km. Heng Chan; Mohawk College

Simplified Block Diagram
Upconverter Preemphasized Baseband Input FM Modulator Mixer BPF RF Out Amp Ch. Combiner RF Oscillator IF Oscillator FM Microwave Transmitter Downconverter Deemphasized Baseband Output FM Detector Mixer BPF RF In Amp Ch. Separator RF Oscillator FM Microwave Receiver Heng Chan; Mohawk College

Notes On FM Microwave Radio System
Baseband signals may comprise one or more of : Frequency-division-multiplexed voice-band channels Time-division-multiplexed VB channels Broadcast-quality composite video or picturephone Wideband data IF carrier is typically 70 MHz Low-index frequency modulation is used Common microwave frequencies used: 2-, 4-, 6-, 12-, and 14-GHz bands. Heng Chan; Mohawk College

Microwave Radio Systems (cont’d)
The distance between transmitter and receiver is typically between 24 to 64 km. Repeaters have to be used for longer distances. To increase the reliability of microwave links, the following techniques can be used: frequency diversity - two RF carrier frequencies space diversity - two or more antennas are used polarization diversity - vertical and horizontal polarization Heng Chan; Mohawk College

Heng Chan; Mohawk College
System Gain System gain for microwave radio link is: Gs (dB) = Pt - Cmin= Fm + Lp + Lf + Lb - At - Ar where Pt = transmitter output power (dBm) Cmin = min. receiver input power (dBm) Fm=fade margin for a given reliability objective (dB) Lp = free-space path loss between antennas (dB) Lf, Lb = feeder, coupling, & branching losses (dB) At, Ar = Tx and Rx antenna gain respectively (dB) Heng Chan; Mohawk College

Introduction To Pulsed Radar
Pulse of energy t Pulse Repetition Time PRT Pulse repetition frequency, PRF = 1/PRT Duty cycle, D = t/PRT Range to target, R = ct/2, where c = speed of light, and t = time between TX pulse and echo return. Dead zone, Rdead, and resolution, DR, are both = ct/2. Resolution can be improved by pulse compression. Heng Chan; Mohawk College

Radar Power & Range Equation
Average power, Pa = Ppt(PRF) = Ppt/PRT = PpD where Pp = peak power. Ideal radar range equation: where PR = signal power returned (W) G = antenna gain l = wavelength of signal (m) s = radar cross section of target (m2) In the real world, losses and noise must be added to above equation. Heng Chan; Mohawk College

Pulsed Radar Block Diagram
Receiver Section Video Amp Video Detector IF Amp Mixer RF Amp Antenna LO Signal Processor T/R Switch Control Section Modulator Timer Display Transmitter Heng Chan; Mohawk College

Heng Chan; Mohawk College
Radar Display Modes N Targets Beam Sweep Target Range Elevation Plan Position Indicator E-Scan Heng Chan; Mohawk College

Heng Chan; Mohawk College
CW Doppler Radar The Doppler effect can be used for determining the speed of a moving target. Microwave Oscillator TX RX Circulator Doppler Mixer v = lfd/2 (m/s) where fd = doppler shift (Hz) l = radar wavelength (m) fd Basic block diagram of CW Doppler radar Heng Chan; Mohawk College

Heng Chan; Mohawk College
FM Doppler Radar Both distance and velocity can be determined if an FM Doppler radar is used. fi Range: TX where a = slope of line or rate of change of fi fd- fo RX fd+ Velocity: t Heng Chan; Mohawk College

Optical Fibre Communications
Advantages over metallic/coaxial cable: much wider bandwidth and practically interference-free lower loss and light weight more resistive to environmental effects safer and easier to install almost impossible to tap into a fibre cable potentially lower in cost over the long term Disadvantages: higher initial cost in installation & more expensive to repair/maintain Heng Chan; Mohawk College

Heng Chan; Mohawk College
Optical Fibre Link Transmitter Input Signal Coder or Converter Light Source Source-to-fibre Interface Fibre-optic Cable Output Fibre-to-light Interface Light Detector Amplifier/Shaper Decoder Receiver Heng Chan; Mohawk College

Types Of Optical Fibre Light ray n1 core n2 cladding
Single-mode step-index fibre no air n1 core n2 cladding Multimode step-index fibre no air Variable n Multimode graded-index fibre Index porfile Heng Chan; Mohawk College

Comparison Of Optical Fibres
Single-mode step-index fibre: minimum signal dispersion; higher TX rate possible difficult to couple light into fibre; highly directive light source (e.g. laser) required; expensive to manufacture Multimode step-index fibres: inexpensive; easy to couple light into fibre result in higher signal distortion; lower TX rate Multimode graded-index fibre: intermediate between the other two types of fibres Heng Chan; Mohawk College

Acceptance Cone & Numerical Aperture
n2 cladding qC n1 core n2 cladding Acceptance angle, qc, is the maximum angle in which external light rays may strike the air/fibre interface and still propagate down the fibre with <10 dB loss. Numerical aperture: NA = sin qc = (n12 - n22) Heng Chan; Mohawk College

Losses In Optical Fibre Cables
The predominant losses in optic fibres are: absorption losses due to impurities in the fibre material material or Rayleigh scattering losses due to microscopic irregularities in the fibre chromatic or wavelength dispersion because of the use of a non-monochromatic source radiation losses caused by bends and kinks in the fibre modal dispersion or pulse spreading due to rays taking different paths down the fibre coupling losses caused by misalignment & imperfect surface finishes Heng Chan; Mohawk College

Absorption Losses In Optic Fibre
6 Rayleigh scattering & ultraviolet absorption 5 4 Loss (dB/km) 3 Peaks caused by OH- ions Infrared absorption 2 1 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 Wavelength (mm) Heng Chan; Mohawk College

Fibre Alignment Impairments
Axial displacement Gap displacement Angular displacement Imperfect surface finish Heng Chan; Mohawk College

Heng Chan; Mohawk College
Light Sources Light-Emitting Diodes (LED) made from material such as AlGaAs or GaAsP light is emitted when electrons and holes recombine either surface emitting or edge emitting Injection Laser Diodes (ILD) similar in construction as LED except ends are highly polished to reflect photons back & forth Heng Chan; Mohawk College

Heng Chan; Mohawk College
ILD versus LED Advantages: more focussed radiation pattern; smaller fibre much higher radiant power; longer span faster ON, OFF time; higher bit rates possible monochromatic light; reduces dispersion Disadvantages: much more expensive higher temperature; shorter lifespan Heng Chan; Mohawk College

Optical Transmitter Circuits
+VCC C1 R2 Data Input Q1 +HV R1 LED Enable C1 R3 Q1 Data Input R1 C2 Enable R2 ILD Heng Chan; Mohawk College

Heng Chan; Mohawk College
Light Detectors PIN Diodes photons are absorbed in the intrinsic layer sufficient energy is added to generate carriers in the depletion layer for current to flow through the device Avalanche Photodiodes (APD) photogenerated electrons are accelerated by relatively large reverse voltage and collide with other atoms to produce more free electrons avalanche multiplication effect makes APD more sensitive but also more noisy than PIN diodes Heng Chan; Mohawk College

Photodetector Circuit
+V R1 Comparator shaper Data Out - - PIN or APD + + - Enable + Threshold adjust Heng Chan; Mohawk College

Bandwidth & Power Budget
The maximum data rate R (Mbps) for a cable of given distance D (km) with a dispersion d (ms/km) is: R = 1/(5dD) Power or loss margin, Lm (dB) is: Lm = Pr - Ps = Pt - M - Lsf - (DxLf) - Lc - Lfd - Ps  0 where Pr = received power (dBm), Ps = receiver sensitivity(dBm), Pt = Tx power (dBm), M = contingency loss allowance (dB), Lsf = source-to-fibre loss (dB), Lf = fibre loss (dB/km), Lc = total connector/splice losses (dB), Lfd = fibre-to-detector loss (dB). Heng Chan; Mohawk College