RF & Microwave References

S-Parameter/Return Loss/Smith Chart Maximum and Minimum

S-parameters (scattering parameters) are a convention for characterizing RF & microwave devices, consisting of reflection and transmission coefficients—familiar concepts to designers. Transmission Resultant VSWR from coefficients are commonly referred to as gains or attenuations, reflection coefficients relate to return losses and VSWRs (voltage standing wave ratios). Conceptually, “s” parameters are like “h”, “y”, or “z” parameters because they describe the inputs and Two Mismatches outputs of a black box. The inputs and outputs are in terms of power for “s” parameters; for “h”, “y”, and “z” parameters, they are voltages and currents. Test Device Component Using the convention that “a” is a signal into a part VSWR’s and “b” is a signal out, the figure below helps to RESULTANT explain “s” parameters. VSWR

2 In this figure, “a” and “b” are the square roots of power; (a1) is the power incident are port 1 and 2 (b2) is the power leaving port 2. The diagram shows the relationship between the “s” parameters and If L is the larger VSWR of two the “a’s” and “b’s”. For example, a signal, a1, is partially reflected at port 1; the rest of the signal is cascaded lossless mismatches transmitted through the device and out of port 2. The fraction of a1 that is reflected at port 1 is s11; and S the smaller, the resultant the fraction of a1 that is transmitted is s21. Similarly, the fraction of a 2 that is reflected at port 2 is VSWR may vary from a mini- s22, and the fraction s12 is trans- mum N = L/S to a maximum mitted. The signal, b1, leaving port 1 is the sum of the fraction X = LS, depending on the spacing between L and S. of a1 that is reflected at port 1 and the fraction of a2 that is transmitted from port 2. Thus, the outputs can be related the the inputs by the equations:

b1=s11a1+s12a2

b2=s21a1+s22a2

when a2= 0 Example: b__1 __b2 s11= s21= a1 a1 If S = 2 and L = 2.5, then X = 5 and N = 1.25. Given any two values, the other two may be found. and when a1= 0

b__1 b __2 s12= s22= a2 a2

Millimeter–Wave Transmission Spectrum Analyzer Digital Modulation Type and Constellation Attenuation Curves Display Range Wavelength (mm) ______+30 dBm DAMAGE LEVEL The atmospheric attenuation of mm- wave signals varies ______0 dBm <1 dB GAIN COMPRESSION greatly, allowing for long-range exploita- ______–40 dBm MAX INPUT FOR SPECIFIED tion by operating in DISTORTION BPSK QPSK Pi/4DQPSK: Two Bits Per Symbol the windows at 35, One Bit Per Symbol Two Bits Per Symbol Symbol Rate = 1/2 Bit Rate 94, 140, and 220 GHz, Symbol Rate = Bit Rate Symbol Rate = 1/2 Bit Rate or 8PSK: Three Bits Per Symbol or for short-range, OPTIMUM OPERATING RANGE Symbol Rate = 1/3 Bit Rate intercept resistant (70 dB, SPURIOUS FREE) communications at Total 44 to 65 GHz. Measurement Range ______–110 dBm NOISE LEVEL (10 kHz BW) Attenuation (dB/km)

______–120 dBm NOISE LEVEL (1 kHz BW)

______–130 dBm NOISE LEVEL (100 Hz BW)

______–140 dBm NOISE LEVEL (10 Hz BW) 16 QAM 32 QAM 64 QAM Four Bits Per Symbol Five Bits Per Symbol Six Bits Per Symbol Frequency (GHz) Typical Values Symbol Rate = 1/4 Bit Rate Symbol Rate = 1/5 Bit Rate Symbol Rate = 1/6 Bit Rate

Microwave Formulae Modulation Quality: Noise Power at

Wavelength (λ) Characteristic Impedance (Z 0) of RF Cable Noise Figure (NFdB) 3 x 1010 λ(centimeters) = ______138 D Z = __ log S_____i /Ni Error Vector Magnitude 0 10 Standard Temperature f NF = 10 log √ ε d dB 10 8 r So /No ______3 x 10 λ(meters) = where εr = relative dielectric constant Where NF = noise figure (dB) f dB Q Magnitude Error (IQ error mag) D = inside diameter of outer Si /Ni = input signal-to-noise ratio where f = frequency (hertz) conductor So /No = output signal-to-noise ratio d = outside diameter of inner Error Vector k = 1.38 x 10-23 joule /k conductor Noise Figure (NFdB) dB (Power and Voltage) Reflection Coefficient ρ R - jx R - jx T = Temperature (K) L L S_____i /Ni P1 VSWR – 1 NFdB = 10 log10 dB(power)= 10 log10 __ Velocity Factor ______Measured B = Bandwidth (Hz) ρ = So /No P2 __1 VSWR + 1 Signal v = __ x 100 Where NFdB = noise figure (dB) √εr where VSWR = Voltage Standing Wave Ratio E1 Si /Ni = input signal-to- dB(voltage)= 20 log10 __ E2 where ε = relative dielectric constant noise ratio r Return Loss in dB Available Noise Power* So /No = output signal-to- dB = 20 log10 ρ where P1 & P2 = system powers P = kTB noise ratio E1 & E2 = system voltages av where ρ = reflection coefficient -21 At 290KPav = 4 x 10 W/Hz = -174dBm/Hz VSWR Reference Signal In deep space kT = -198dBm/Hz _____1 + ρ VSWR = * Noise figure is defined when input is terminated at 290 Kelvins. 1 – ρ Phase Error (IQ error phase) where ρ = reflection coefficient I

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