ELEN726 Microwave Measurements: Theory & Techniques. Lecture 3 Amplifier & Mixer Measurements

Transcription

1 ELEN726 Microwave Measurements: Theory & Techniques Lecture 3 Amplifier & Mixer Measurements References: Principles of Microwave Measurements by GH Bryant Peter Peregrinus Ltd. U.K. on behalf of IEE. 1988

2 Plan for Today Review & Questions from Lecture 2. Amplifier Introduction, Characteristics & Applications Mixers Introduction, Characteristics & Applications Definition & Measurement of: Noise Figure, Te, G/T Definition & Measurement for Amplifiers: Gain, Isolation, VSWR, Group delay P_1 db, Psat, IMD Products and IP3 AM-PM, ACPR, THD, NPR Definition & Measurement for Mixers: Conversion Loss, P_1 db, Image Rejection, Spurious A Signal Generators Home Assignment

3 RF Connectors Types: SMA, N, APC7, 3.5mm, 2.92mm, K, V, 1.85, 1mm, GPO, GPPO, BNC, TNC, SMB, SMC, OSSM, SSMA

4 Block diagram (RF Comm. System)

5 Amplifier Characteristics Gain S21 VSWR S11, S22 Isolation S12 Efficiency Noise Figure Non-linearity P_1 db Psat IM IP3.. Types LNA Power Amp Driver Amp Narrowband Wideband Single Ended Balanced Amp Distributed Amplifiers

6 Technologies for Amplifiers Si BJT MOSFET JFET LDMOS GaAs FET Pseudomorphic HEMT (PHEMT) InP HEMT Metamorphic HEMT (mhemt) Heterojunction Bipolar Transistor (HBT) SiGe HBT InP HBT SiC MESFET GaN HEMT Monolithic Microwave Integrated Circuit (MMIC)

7 Amplifier Efficiency Vdc, Idc Pin Pout Drain efficiency: Ratio of RF output power to DC input power: η d = Pout/Pdc where Pdc = Vdc x Idc Power-added efficiency (PAE): considers the RF drive power (Pin) by subtracting it from the output power: Overall efficiency η PAE η OE = (Pout Pin)/Pdc. = Pout/(Pdc + Pin)

8 Harmonic Distortion.

9 Harmonic Distortion Input 1V (+13 dbm, 50 ohm) 2V (+19 dbm, 50 ohm) G = 20 db Output Fund: 10 V (+33 dbm) 2 nd H: 10 mv (-27 dbm) 3 rd H: 1 mv (-47 dbm) Fund: 20V (+39 dbm) 2 nd H: 40 mv (-15 dbm) 3 rd H: 8 mv (-29 dbm)

10 Intermodulation

11 3rd IM Products Intermodulation Distortion (IMD): The 3 rd order IMD product is usually defined as the ratio of the power in one of the third order tones to that of one of the main tones. IP3 = Pout Delta 2 This equation is valid in the linear region of the P in vs P out plot (next slide). Typically measurement point used is >10 db below P_1 db.

12 Intermodulation Products Pout (dbm) ` a db Pin (dbm)

13 Slopes of the three lines are 1:1, 2:1 and 3:1. IP3 = Po + 3f nd & 3 rd Order Intercept Point IP3 Where represents the vertical distance between the fundamental and the third order modulation products in db at the measurement point. IP2=P o Where represents the vertical distance between the fundamental and the second order modulation products in db at the measurement point.

14 Spectral Regrowth Spectral Regrowth is the tendency for the output spectrum of a non-linear amplifier to grow shoulders. It is an undesirable effect, which corrupts a frequency band (the adjacent channel) outside the channel of operation. Spectral regrowth depends on the degree of non-linearity of the amplifier. when a PA is fed with digitally modulated signals, the variations in the amplitude of the modulation envelope also have an impact on spectral regrowth. The shape of the modulation envelope is highly dependent on the modulation format itself. More constant envelopes such as those obtained with GMSK modulation, for example, are less prone to the spectral regrowth effect.

15 Adjacent Channel Power Ratio (ACPR) ACPR, a measure of spectral growth, is the ratio of the power in a specifies band outside the signal bandwidth to the rms power in the signal. Locations and bandwidths of the measurements depend upon the standards. ACPR as a function of Input power ACPR EDGE Standard

16 Error Vector Magnitude (EVM): EVM is a convenient measure of how non-linearity interferes with the detection process. EVM is defined as the distance between the desired and actual signal vectors, normalized to a fraction of the signal amplitude. Often, both peak and rms errors are specified. Q Magnitude Error (IQ error mag) Test Signal { Error Vector φ Ideal (Reference) Signal Phase Error (IQ error phase) I

17 EVM v is the ideal symbol vector, Caused by: carrier leakage, low w is the measured symbol vector, image rejection ratio, phase noise etc. w-v is the magnitude error, θ is the phase error, e=w v) is the error vector, and e/v is the EVM. EVM is normalized by v, which is expressed as a percentage. Analytically, RMS EVM over a measurement window of N symbols is defined as where Ij is the I component of the j-th symbol received, Qj is the Q component of the j-th symbol received, ~Ij is the ideal I component of the j-th symbol received, ~Qj is the ideal Q component of the j-th symbol received.

18 EVM (contd) The error vector magnitude is equal to the ratio of the power of the error vector to the RMS power of the reference. It is defined in db as: where P error is the root mean square power of the error vector, and P reference is the root mean square power of ideal transmitted signal. EVM is defined as a percentage in a compatible way: with the same definitions

19 THD & NPR Total Harmonic Distortion (THD) THD is typically the ratio (in db or dbc) of the rms sum of the first four harmonics of the input signal to the fundamental itself. Noise-Power Ratio (NPR) NPR is a measure of the linearity of PAs for broadband and noise-like signals. The PA is driven with Gaussian noise with a notch in one segment of its spectrum. Nonlinearities cause power to appear in the notch. NPR is the ratio of the notch power to the total signal power.

20 AM to PM Conversion Measure of phase deviation caused by amplitude variations AM (db) Amplitude Power sweep Mag(Am in ) DUT AM can be undesired supply ripple, fading, thermal AM can be desired: modulation (e.g. QAM) PM (deg) Test Stimulus Time Amplitude Q AM - PM Conversion = AM (db) Mag(AM out ) Mag(Pm out ) (deg/db) Mag(Am in ) PM (deg) Output Response Time Mag(Pm out ) AM to PM conversion can cause bit errors I

21 Measuring AM to PM Conversion 1:Transmission Log Mag 1.0 db/ Ref db 2:Transmission /M Phase 5.0 deg/ Ref deg Ch1:Mkr dbm db Ch2:Mkr db 0.86 deg 1 2 Use transmission setup with a power sweep Display phase of S21 AM - PM = 0.86 deg/db 2 Start dbm Start dbm 1 CW MHz CW MHz 1 Stop 0.00 dbm Stop 0.00 dbm

22 Noise & Noise Figure

23 Noise Figure Noise Figure is a figure of merit describing the internal noisiness of a transducer. It allows specifying noise performance independent of other parameters like gain, frequency, bandwidth etc. NF allows to specify the noise performance from a device to component to sub-system to a system. It is generally represented as F (db). The weakest signal that can be detected in a Rx is determined by the noise added by the receiver.

24 Thermal Noise Vn 2 = 4kTBR k = 1.38 x Joules/K is Boltzman s constant At Microwaves noise power is more appropriate: Pavail = Vn 2 /4R = ktb At standard temp of 290 deg K: kto = 4 x = -174 dbm/hz R + jx L R - jx L Thermal Noise is present in both active and passive devices.

25 Noise Figure (S/N) in Na, G (S/N) out (S/N) in F = (S/N) out (S/N) in = S in / N in Ts = 290 O K (S/N) = S out out / N out = S out / (N a + G. N in ) F = (N a + G. N in ) / (G.N in ) With N in = ktb and G = S out /S in F db = 10 Log (F) NF is the ratio of the total noise power out to that portion of the output due to the noise at input, all at 290 o K.. (1) Na = kt o BG (F-1).. (2)

26 Effective Input Noise Temperature Te Ts Na Np = Na + kgbts Ts Te Na=0 Np = kgb(te + Ts) Te is the temp. of a factitious additional source resistor that produces the same noise power at the output of a noise free two port as does the two port being tested without the additional source resistance. Te is preferred for low noise devices as it is a more sensitive indicator when Na is small. Na = kgb Te & from eqn. 2 on last slide: Na = (F-1) ktogb Te = To (F-1) (3) Or F= 1 + Te / To.(4)

27 Measurement of Noise Figure Tc Th N2 kt e B N G + kt h B N G Y = = N1 kt e B N G + kt c B N G T e + T h = T e + T c Na,Te N2 N1 Na N1, N2 T h -YT c Or Te = Y-1 & As F= 1 + Te / To (T h /T o 1) Y(T c /T o -1) F = Y-1 If T c = T o (Th-To)/To F= (N2/N1)-1

28 Effect of Second Stage Contribution Using eqn. 2: Na = (F-1) kt o BG Na 1 = (F 1-1) kt o BG 1 Na 2 = (F 2-1)kT o BG 2 Total Noise Power Out Cascaded Noise Figure F = Noise Power Out due to noise power at input Using equations above: kt = o BG 1 G 2 + (F 1-1) kt o BG 1 G 2 +(F 2-1)kT o BG 1 G 2 kt o BG 1 G 2 F Or F = F (5) G 1

29 Cascaded Effective Noise Temperature Noise P in = kt s B T e1 T e1 G 1 G 2 Noise P out Noise added by stage 1: kg 1 BTe 1 Noise at the output of 1st stage: kg 1 B(Te 1 +T s ) Noise at the output of 2 nd stage: kg 2 BTe 2 + kg 1 G 2 B(Te 1 + T s ). (9) If the cascaded Gain G 12 = G 1. G 2 and cascaded effective noise temp. is Te 12 Noise P out is also = kg 12 BTe 12 + kg 12 BT s = kg 1 G 2 B(Te 12 + T s ).. (10) Equating (9) and (10): kg 1 G 2 B(Te 12 + T s ) = kg 2 B (Te 2 + G 1 Te 1 + G 1 T s ) Te Or Te 12 = Te (11) G 1

30 Equivalence of the NF & Te Cascading Relations Te Te 12 = Te (11) G 1 Te 12 F 12 = T o Te F 12 = T o Te F 12 = T o + 1 or Te 12 = (F 12 1) T o + 1 or Te 2 = (F 2 1) T o + 1 or Te 1 = (F 1 1) T o Substituting in (11): (F 2 1) T o (F 12 1) T o = (F 1 1) T o G 1 Or F = F F 2-1 G 1

31 Gain to Temperature Ratio (G/T) G/T is a figure of merit for a satellite or radio astronomy receiver system, including the antenna, that portrays the operation of the total system. The numerator is the antenna gain, the denominator is the operating noise temperature of the receiver. The ratio is usually expressed in db, for example, 10log(G/T). G/T is often measured by comparing the receiver response when the antenna input is a hot celestial noise source to the response when the input is the background radiation of space ( 3K).

32 Gain Measurement using NF F F = F G 1 To find F1 you need to measure F12, F2 & G1. Fortunately information on G1 is in the slope of the noise power vs. source temp. graph N2 Calibration (Measurement System) N2 DUT (DUT + Measurement System) N1 Na N1 Na Tc Th Tc Th N2 - N1 kg 2 B = Th - Tc N2 - N1 G1 = Th - Tc N2 - N1 Th - Tc kg 1 G 2 B = N2 - N1 Th - Tc

33 Noise Sources Three basic Types Thermal Very Accurate Low SWR/SWR variation Inconvenient: Liquid N2 required. Two connections Waveguide Gas-Discharge High Voltage Power Source needed Flat with frequency Solid State Noise generators Wide Frequency range (10MHz to 50 GHz) ON> Short, OFF> Capacitive. Th ~ 10,000K Tc = room temp. Requires pad for matching Low Power Dissipation Requires High Stability Power Supply Requires calibration with frequency ENR proportional to diode current

34 ENR A noise generator property calculated from the hot and cold noise temperatures (Th and Tc) using the equation ENR db =10 log T h T c (7) T 0 where To is the standard temperature of 290K. Noise temperatures Th and Tc should be the effective noise temperatures. (See Effective Noise Temperature) [25]. The ENR calibration of diode noise sources assumes Tc=To. An ENR of 0 db corresponds to Th = 580K and Th of 100 C (373K) corresponds to an ENR of 5.43 db. From slide 19, If Tc = To: (T h /T o 1) ENR F = = Y-1 Y-1 Also if Tc = To T h = {10 ENR[(dB)/10 + 1} x 290 F db = ENR db -- Log (Y-1)

35 Measurement Errors

36 Mixers Up Converters & Down Converters

37 Mixers Definition Mixers are used for frequency conversion and are critical components in modern radio frequency (RF) systems. The ideal mixer is a device which multiplies two input signals. If the inputs are sinusoids, the ideal mixer output is the sum and difference frequencies given by Typically, either the sum, or the difference, frequency is removed with a filter.

38 Types of Mixers

39 Mixer Characteristics Conversion Loss is the ratio of the output signal level to the input signal level expressed in db. In a single sideband system, only one sideband is used; therefore 3 db of loss is theoretical. The additional loss is diode and transformer loss. Isolation is the amount of "leakage" or "feed-through" between the mixer ports. Noise Figure is the signal-to-noise ratio at the input divided by the signal-to-noise ratio at the output expressed in db. Conversion Compression is the RF input level above which the RF versus IF output curve deviates from linearity. Dynamic Range is the amplitude range over which a mixer can operate without degradation of performance. It is bounded by the conversion compression point for high input signals, and by the noise figure of the mixer for low level input signals. Image Rejection Intercept Point, measured in dbm, is a figure of merit for intermodulation product suppression. A high intercept point is desirable. Two types are commonly specified: input ;and output intercept point (IIP and OIP, respectively). Voltage Standing Wave Ratio (VSWR) is the measure of mismatch offered to the system by the mixer, and is usually specified over a given bandwidth as a function of LO power and temperature.

40 Mixing Products

41 Conversion Loss & P_1 db

42 Mixer Noise Figure f LO f s f IF f IF f IF f IF f s f i f LO B B Frequency If Gs and Gi are the conversion gains for signal and image channels, the output S/N ratio is: So -- = So No kb(to + Te)(Gs + Gi) where Te is assumed to be same in both channels Si Si Si/Ni -- = F = = No kb(to+te)(gs+gi) = (11) Ni ktob So/No Gs Ni kbtogs or F = To Th Gi ( ) To Gs This is called Single Sideband NF as the signal is restricted to fs. In practice noise source is both signal & noise. Using Gs + Gi in place of Gs (eqn.11), observed signal is DSB and SSB NF = DSB NF + 3dB

43 DSB vs SSB Noise Figure

44 DSB to SSB Conversion

45 Receiver Sensitivity The smallest signal that a receiver can reliably detect. Sensitivity specifies the strength of the smallest signal at the input of a network that causes the output signal power to be M times the output noise power where M must be specified. M represents So/No and M=1 is used commonly. For a source temperature of 290K, the relationship of sensitivity to noise figure is Si = MkToBF Or In dbm Si (dbm) = 174 dbm + F(dB) + 10 log B + 10 log M Thus sensitivity is related to noise figure once the bandwidth is known.

46 Spurious Response of a Mixer

47 Spurious Rule of Thumb

48 Mixer Spurious Calculation Programs: The Engineers Club Demo 3. Microwaves101.com 4. rfcafe.com

49 IQ Mixer

50

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