Appendix Power Transfer Basics Low frequencies I wavelengths

Appendix

Power Transfer Basics Low frequencies + I - wavelengths >> wire length l current (I) travels down wires easily for efficient power transmission l measured voltage and current not dependent on position along wire l High frequencies wavelength » or << length of transmission medium l need transmission lines for efficient power transmission l matching to characteristic impedance (Z 0) is very important for low reflection and maximum power transfer l measured envelope voltage dependent on position along line l

Transmission Line Basics Zo determines relationship between voltage and current waves l Zo is a function of physical dimensions and l Zo is usually a real impedance (e. g. 50 or 75 ohms) l er Waveguide a w b Twisted-pair Coaxial h er h w 1 w w 2 Coplanar Microstrip Characteristic impedance for microstrip transmission lines (assumes nonmagnetic dielectric)

Power Transfer Efficiency RS RL RL / R S Maximum power is transferred when RL = RS

Power Transfer Efficiency For complex impedances, maximum power transfer occurs when ZL = ZS* (conjugate match) Zs = R + j. X Rs +j. X -j. X RL ZL = Zs* = R - j. X At high frequencies, maximum power transfer occurs when RS = RL = Zo Zo Zo

Smith Chart Review . +j. X 90 o Polar plane 1. 0. 8. 6 +R ¥ ® 0 0 -j. X . 4 + 180 o - . 2 0 o ¥ Rectilinear impedance plane -90 o Constant X Z L = Zo G= Smith Chart maps rectilinear impedance plane onto polar plane 0 Z L = 0 (short) G= 1 Constant R ± 180 O Z L= G =1 (open) 0 O Smith Chart

Lightwave Analogy to RF Energy Incident Transmitted Reflected Lightwave RF

Transmission Line Terminated with Zo Zo = characteristic impedance of transmission line Zs = Zo Zo V inc Vrefl = 0! (all the incident power is absorbed in the load) For reflection, a transmission line terminated in Zo behaves like an infinitely long transmission line

Transmission Line Terminated with Short, Open Zs = Zo V inc Vrefl In phase (0 ) foro open o Out of phase (180 ) for short For reflection, a transmission line terminated in a short or open reflects all power back to source

Transmission Line Terminated with 25 W Zs = Zo ZL = 25 W V inc Vrefl Standing wave pattern does not go to zero as with short or open

Device Characteristics Devices have many distinctive characteristics such as: l electrical behavior èDC power consumption èlinear (e. g. S-parameters, noise figure) ènonlinear (e. g. distortion, compression) l physical specifications èpackage type èpackage size èthermal resistance l other things. . . ècost èavailability When selecting parts for design, characteristics are traded-off Let's look at important electrical characteristics for RF design. . . 100 p

High-Frequency Device Characterization DUT Incident R Transmitted B Reflected A TRANSMISSION REFLECTION Reflected Incident = SWR S-Parameters S 11, S 22 Reflection Coefficient G, r A Transmitted R Incident Return Loss Impedance, Admittance R+j. X, G+j. B = B R Group Delay Gain / Loss S-Parameters S 21, S 12 Transmission Coefficient T, t Insertion Phase

Reflection Parameters Reflection Coefficient G Vreflected = = Vincident Return loss = -20 log(r), No reflection (ZL = Zo) 0 ¥ d. B 1 r r = F G Emax Emin r = ZL - ZO Z L + ZO Voltage Standing Wave Ratio Emax VSWR = Emin = 1+r 1 -r Full reflection (ZL = open, short) 1 RL 0 d. B VSWR ¥

Transmission Parameters V Incident DUT Transmission Coefficient = T = Insertion Loss (d. B) = - 20 Log Gain (d. B) = 20 Log Insertion Phase (deg) = V Transmitted V V Trans VTransmitted V Incident V V Trans = = - 20 log Inc = 20 log t Inc V V Trans Inc tÐf = f t

Group Delay (GD) Frequency w Dw Phase f -d f dw f = Group delay ripple to Average delay Df Group Delay (t g) tg = Frequency -1 360 o * df df in radians/sec in degrees f in Hertz (w = 2 p f) average delay indicates electrical length l GD ripple indicates distortion l aperture of measurement is very important èaperture is frequency-delta used to calculate GD èwider aperture: lower noise / less resolution ènarrower aperture: more resolution / higher noise l

Phase versus Frequency R 50 W A Phase Difference between A and R Frequency

Phase versus Frequency R 50 W DUT Phase Difference between A and R Frequency A

Phase versus Frequency R 50 W DUT Phase Difference between A and R Frequency A

T/R Versus S-Parameter Test Sets Transmission/Reflection Test Set S-Parameter Test Set Source Transfer switch R R B A Port 1 Port 2 Fwd l l l Port 2 Port 1 Fwd DUT RF always comes out port 1 port 2 is always receiver response, one-port cal available B A l l l DUT Rev RF comes out port 1 or port 2 forward and reverse measurements two-port calibration possible

Response Calibration DUT THRU Source Load Source Reference DUT Measurement errors due to mismatch Load

Two-Port Calibration Two-port calibration corrects for all major sources of systematic measurement errors R Directivity A B Crosstalk DUT Frequency response l l reflection tracking (A/R) transmission tracking (B/R) Source Mismatch Load Mismatch Six forward and six reverse error terms yields 12 error terms for two-port devices

Thru-Reflect-Line (TRL) Calibration TRL calibration was developed for non-coaxial microwave measurements Advantages microwave cal standards easy to make (no open or load) l based on transmission line of known length and impedance l do not need to know characteristics of reflect standard l Disadvantages impractical length of RF transmission lines l fixtures usually more complicated (and expensive) l 8: 1 BW limitation per transmission line l

Characterizing Unknown Devices Using parameters (H, Y, Z, S) to characterize devices: gives us a linear behavioral model of our device l measure parameters (e. g. voltage and current) versus frequency under various source and load conditions (e. and open circuits) l compute device parameters from measured data l now we can predict circuit performance under any source and load conditions l H-parameters V 1 = h 11 I 1 + h 12 V 2 I 2 = h 21 I 1 + h 22 V 2 h 11 = V 1 I 1 V 2=0 (requires short circuit) h 12 = V 1 V 2 I 1=0 (requires open circuit)

Why Use S-Parameters? relatively easy to obtain at high frequencies èmeasure voltage traveling waves with a vector network analyzer èdon't need shorts/opens which can cause active devices to oscillate or self-destruct l relate to familiar measurements (gain, loss, reflection coefficient. . . ) l can cascade S-parameters of multiple devices to predict system S 21 Incident Transmitted performance a 1 b 2 l can compute H, Y, or Z parameters from S-parameters S 11 if DUT Reflected S 22 desired Port 2 Port 1 Reflected b 1 l can easily import and use S-parameter files in our electronic-simulation a 2 Incident S Transmitted 12 tools l b 1 = S 11 a 1 + S 12 a 2 b 2 = S 21 a 1 + S 22 a 2

Measuring S-Parameters a 1 b 1 S 21 = Reflected Incident Transmitted Incident b 2 = a 1 a 2 = 0 S 22 = a 2 = 0 S 12 = a 1 = 0 Z 0 b 1 Transmitted Reflected Incident Transmitted Incident S 22 DUT Load DUT Reflected b 1 = a 1 b 2 Transmitted 21 Z 0 S 11 Forward S 11 = S Incident b 1 = a 2 b 2 Reflected S 12 b 2 = a 2 Reverse a 1 = 0

Equating S-Parameters with Common Measurement Terms S 11 = forward reflection coefficient (input match) S 22 = reverse reflection coefficient (output match) S 21 = forward transmission coefficient (gain or loss) S 12 = reverse transmission coefficient (isolation) Remember, S-parameters are inherently linear quantities -- however, we often express them in a log-magnitude format

Going Beyond Linear Swept-Frequency Characterization So far, we've only talked about linear swept-frequency characterization (used for passive and acti devices). Two other important characterizations for active devices are: nonlinear behavior l noise figure l

Linear Versus Nonlinear Behavior A * Sin 360° * f ( t - t ) ° A Linear behavior: input and output frequencies are the same (no additional frequencies created) loutput frequency only undergoes magnitude and phase change l Time to Sin 360° * f * t A Time f 1 Input Frequency Output DUT Nonlinear behavior: f 1 output frequency may undergo frequency shift (e. g. with mixers) ladditional frequencies created (harmonics, intermodulation) l Frequency Time f 1 Frequency

Measuring Nonlinear Behavior Most common measurements: l using a spectrum analyzer + source(s) èharmonics, particularly second and third èintermodulation products resulting from two or more RF carriers l using a network analyzer and power sweeps ègain compression RL 0 d. Bm èAM to PM conversion 8563 A LPF SPECTRUM ANALYZER ATTEN 10 d. B / DIV 9 k. Hz - 26. 5 GHz DUT CENTER 20. 00000 MHz RB 30 Hz VB 30 Hz SPAN 10. 00 k. Hz ST 20 sec

Noise Figure (NF) Gain DUT Si/Ni Measure of noise added by amplifier l NF = 10 log [(Si/Ni) / (So/No)] l Perfect amp would have 0 d. B NF l So/No

Y-factor Technique for NF Measurements Nout = Na + k. Ts. BG G, Na Amplified Input Noise Added Noise Zs @ Ts = k. Ts. B + 28 V Th (noise source on) => N 2 (at amplifier Noise Power Output (Nout) Excess Noise Source output) Tc (noise source off) => N 1 (at amplifier ENR (d. B) output) Y = N 2/N 1 NF (d. B) = ENR (d. B) - 10 log (Y-1) N 2 N 1 Slope = k. GB Na Th Tc Source impedance temperature

AM to PM Conversion

Measuring AM to PM Conversion use transmission setup with a power sweep ldisplay phase of S 21 l AM to PM = 0. 727 deg/d. B l

Heat Sinking for power devices, a heat sink is essential to keep Tjunction low l heat sink size depends on material, power dissipation, air flow, and T ambient l ridges or fins increase surface area and help dissipate heat l usually device attaches directly to heat sink (flange mounts help) l l bolt device in place first, then solder heat sink