Microwave Measurement Techniques

Home , Ammeter, Frequency counter, Oscilloscope, Voltmeter

A. Nassiri - ANL

Massachusetts Institute of Technology RF Cavities and Components for Accelerators USPAS 2010

• P• n Pn • • Noisy BPF Noiseless,

R T0 k R ≡ R 00 k T0 k, B R

lossless BPF •

• • Load • Load

2  νn  νn Pn =  R = = kTB  2R  4R

The maximum power delivered from the noisy resistor is Pn= kTB, which is considered equally across an entire microwave band.

A resistor temperature at 3000 k, noise power for a 10kHz bandwidth -17 receiver → Pn =4.14 × 10 W = -176dBW= -146dBm

At the standard temperature of 2900 k, the noise power available from a lossy passive network in a 1Hz bandwidth is -174dBm/Hz.

Massachusetts Institute of Technology RF Cavities and Components for Accelerators USPAS 2010 2 Signal-to-noise ratio (SNR)

S Ps =10log Difficult to measure N dB Pn

S + N P + P =10log s n Measurable quantity N dB Pn

A receiver produces a noise power of 200mW without signal, as signal is applied, the output level becomes 5W.

S + N P + P 5 =10log s n =10log =14dB N dB Pn 0.2

Massachusetts Institute of Technology RF Cavities and Components for Accelerators USPAS 2010 3 Noise figure

A figure of merit to measure the degradation of SNR of a system

P = S + N i i i P0 = S0 + N0

R,T Noisy 0 network Si R G,B,T Load

(S N )i NF = ≥1 NFdB =10log NF ≥ 0dB (S N )o

For a passive device with G=1/L and in thermal equilibrium at the temperature T, N0 = kTB = Ni , So =GSi , (S N ) S N NF = i = 0 i = L (S N )o S i N o

Massachusetts Institute of Technology RF Cavities and Components for Accelerators USPAS 2010 4 An amplifier with input signal 100µW and the noise power is 1µW. The amplified signal is 1W with noise power 30mW. 1000000 signal gain =10log = 40dB 100 30000 noise gain =10log = 44.7dB > 40dB 1 (S N )i 100 1 NF = = = 3 >1 NFdB = 4.7dB > 0dB (S N )o 1000 30

An amplifier with NF 6dB has an input SNR=40dB,

(S N )i S S NF = → = − NFdB = 40 − 6 = 34dB (S N )o N o dB N i dB

Massachusetts Institute of Technology RF Cavities and Components for Accelerators USPAS 2010 5 Equivalent noise temperature: the absolute temperature to generate the same noise power, not the physical temperature of the device equivalent noise temperature Te ≡ Pn /kB

Pn P • n White noise R source 0 Load ≡ R T e k R • (S N ) R NF = i (S N ) Pi=Si + Ni P0=S0 + N0 o S Gk(T +T ) = i 0 e B Noisy network kT B GS R, T0 R 0 i Si G,B, Te Load T =1+ e ≥1 T0

→Te = (NF −1)T0

Massachusetts Institute of Technology RF Cavities and Components for Accelerators USPAS 2010 6 NF of a cascaded circuit

G1, F1 G1, F1 • • • G1, F1

(S N ) S N NF = i = i 0 (S N ) S N o 0 i A three-stage amplifier Stage power gain noise figure  N N kT0B∏Gi k(NF1 −1)T0B∏Gi 1 10 10dB 2 3dB 1  =  i =1 + i =1 N kT B kT B 2 20 13dB 4 6dB G  0 0 ∏ i  3 30 14.8dB 6 7.8dB i =1  N  k(NF2 −1)T0B∏Gi  Total gain=6000=37.8dB + i =2 +  kT0B  Total NF=2+[(4-1)/10]+[(6-  k(NF −1)T BG 1)/(10×20)]=2.325=3.66dB + N 0 n  kT0B 

Massachusetts Institute of Technology RF Cavities and Components for Accelerators USPAS 2010 7 Frequency measurements

Two approaches: using frequency counter to measure frequency directly, and using probe to measure the wavelength in a transmission line.

Frequency counter approach

(1) Basic principle: direct counting <500MHz

Input Signal Conditioner Main Count Display Gate Chain Time Gate Base Generator

(2) Using frequency down-conversion techniques for microwave signals

. Pre-scaling: divider circuit <2GHz

Massachusetts Institute of Technology RF Cavities and Components for Accelerators USPAS 2010 8 .Transfer oscillator down-conversion: use PLL to relate the harmonic relationship between the low frequency oscillator and the input microwave signal > 40GHz

PSD Input signal Power divider PL CCT fs  FIF1 To counter Comb generator

fVCO fS = NfVCO-fIF1

Comb generator

fVCO ± fo F fs IF1   FIF2 FIF1 ± Nfo To ratio counter

Massachusetts Institute of Technology RF Cavities and Components for Accelerators USPAS 2010 9 Harmonic heterodyne: use mixer to harmonically down convert the input microwave signal <20GHz

IF amp

Input signal Fs ± Kfi = fIF To counter f  s fIF

Kfi bus YIG pin switch control  counter filter

fi Comb generator multiplier Microprocessor

From counter time base fs = Kfi +fIF

Massachusetts Institute of Technology RF Cavities and Components for Accelerators USPAS 2010 10 Wavelength measurement approach

Gunn Oscillator PS SWR Meter

PS SWR

Fixed short Gunn Oscillator Variable Slotted Line Attenuator circuit

35dB •

2 2 2π 2π 2 2  2π  2π kc = ,λc = 2a,β = = k − kc =   −   λc λg  λ   λc 

2 2  1   1  λ → =   + Measure g f c      λg   2a 

Massachusetts Institute of Technology RF Cavities and Components for Accelerators USPAS 2010 11 Distance between two adjacent minima is 1.9cm in a WR-90 waveguide.

90 λg = 2×1.9cm = 3.8cm, a = × 2.54cm = 2.29cm 100 2 2  1   1  =   + f c      λg   2a  2 2  1   1  = 3×1010cm / sec   +   =10.26 GHz  3.8cm   2× 2.29cm 

Massachusetts Institute of Technology RF Cavities and Components for Accelerators USPAS 2010 12 Wavemeter method

. Wavemeter structure

Resistive material

Piston Cavity

Massachusetts Institute of Technology RF Cavities and Components for Accelerators USPAS 2010 13 Operating principle Cavity Input Output nλ d = g 2 Input b Output

Transmission type Microwave Power Reaction type Meter Standing wave indicator Cavity frequency meter Variable precision attenuator Detector probe Microwave Source 1KHz Square Thermistor mount Wave Modulation Variable flap attenuator Slotted line

Massachusetts Institute of Technology RF Cavities and Components for Accelerators USPAS 2010 14 Detection devices

Power detector: bolometer (thermistor and barretter), thermocouple voltage detector: crystal detector, Schottky barrier diode, GaAs barrier diode

Thermistor: a metallic-oxide component with a negative temperature coefficient of resistance

Barretter: a short length of platinum or tungsten wire with a positive temperature coefficient of resistance

Massachusetts Institute of Technology RF Cavities and Components for Accelerators USPAS 2010 15 Detection devices Thermocouple: a pair of dissimilar metal (Sb-Bi) wires joined at one end (sensing end) and terminated at the other end (reference end). The difference in temperature produces a proportional voltage.

Crystal detector: use the diode square-law to convert input microwave power to detector output voltage Diode Matching Low-pass Filter • Circuit • Microwave Low Input Frequency Output DC Return

DC return is as a ground for diode and an RF choke.

Massachusetts Institute of Technology RF Cavities and Components for Accelerators USPAS 2010 16 Detection devices

Schottky barrier or GaAs barrier diode: high sensitivity noise equivalent power (NEP): the required input power to produce, in 1Hz bandwidth, an output SNR = 1 tangential sensitivity (TSS): the lowest detectable microwave signal power TSS NEP = ,∆f : Vedio Bandwidth 2.5 ∆f

Massachusetts Institute of Technology RF Cavities and Components for Accelerators USPAS 2010 17 Power Measurements

Difficulty in measuring voltage or current at microwave frequencies → power measurement simpler and more precise

Power range: low power <0dBm, medium power 0dBm~40dBm, high power >40dBm

power detector sensitivity: diode ~-70dm, thermistor ~-20dBm

Thermistor power meter •A • R Wheatstone Bridge R Balance AC Ammeter Adust C • A • D v 10-kHz AC P0 R Source P1 RT Voltmeter • • Microwave B Power in

Massachusetts Institute of Technology RF Cavities and Components for Accelerators USPAS 2010 18 Power measurement arrangement . Low power case

Consider desired frequency spectrum, circuit mismatch, sensor mismatch, sensor safe margin, accuracy, calibration

Generator Power RF Out Meter

LPF Attenuator Power DUT or BPF (optional) Sensor

Massachusetts Institute of Technology RF Cavities and Components for Accelerators USPAS 2010 19 Power measurement arrangement Medium power case: use directional coupler or attenuator at the DUT (device under test) output Thermistor Generator (0 dBm) Power Meter Power 1 Watt 10 dB Supply Circulator 50Ω Attenuator (+10 dBm) 1 Watt (+30 dBm) 2 Ω 1 Watt 3 dB 1 3 2 Watts 50 Attenuator Amplifier 20 dB Coupler under test Generator Power Thermistor Supply Circulator 50Ω (0 dBm) Power Meter 1 Watt (+30 dBm) 1 Watt 3 dB 30 dB 2 Watts 50Ω Attenuator Attenuator Amplifier under test

Massachusetts Institute of Technology RF Cavities and Components for Accelerators USPAS 2010 20 Power measurement arrangement High power case: use directional coupler in reverse direction Power Meter (0 dBm) Thermistor Mount

30 dB Maximum full Attenuator scale +10 dBm (2 Watts)

(+30 dB) 100 watts (+50 dBm) 1 2 20 dB Directional Power Coupler Amplifier 3

50 Ω, 1W Termination

Massachusetts Institute of Technology RF Cavities and Components for Accelerators USPAS 2010 21 Attenuation Measurements

P3 Insertion Loss P P1 2

Source Component Load

P4 P1: power to the load without DUT P2: power to the load after inserting DUT P3: power dissipated inside DUT P4: power reflected from DUT

P1 ILdB =10log = P1(dBm ) − P2(dBm ) P2

Massachusetts Institute of Technology RF Cavities and Components for Accelerators USPAS 2010 22 If Γ: DUT reflection coefficient and T: DUT transmission coefficient, 2 2 2 1− Γ ILdB = −10logT = −10logT 1− Γ 2 T 2 = −10log(1− Γ 2 )−10log 1− Γ 2 P − P P = −10log 1 4 −10log 2 P1 P1 − P4 = loss due to reflection + loss due to transmission

P1 P1 – P4 P2

P4 Insertion loss is the characteristics of DUT itself. As input port and output ports are matched, IL= attenuation. Massachusetts Institute of Technology RF Cavities and Components for Accelerators USPAS 2010 23 VSWR measurements

SWR Meter

SWR

Slotted Line Microwave Source Load (1 kHz AM) •

If E probe penetrates too far into the slotted line, → disturb the field distribution and detected signal too strong to drive the detector out of its square-law region.

Massachusetts Institute of Technology RF Cavities and Components for Accelerators USPAS 2010 24 S- Parameters

Problems to use Z- , Y- or H- parameters in microwave circuits  Difficult in defining voltage and current for non-TEM lines  No equipment available to measure voltage and current in complex value as oscilloscope  Difficult to make open and short circuits over broadband  Active devices not stable as terminated with open or short circuit. S-parameters of a two-port network

Z0 2-Port Z V V R = Z 0 1 Device 2 Z0 L 0

2V1

I    a1 1  S21 b2 • •

S V1 11 V2 S22 b I2 1  •  •   S12 a2 Z in Z out

Massachusetts Institute of Technology RF Cavities and Components for Accelerators USPAS 2010 25 Definition of S- Parameters

+ a1 =V1 Z 0 : incident (power) wave at port 1 − b1 =V1 Z 0 : reflected (power) wave at port 1 + a2 =V2 Z 0 : incident (power) wave at port 2 − b2 =V2 Z 0 : reflected (power) wave at port 2

+ − + − + − + − V1 V1 V2 V2 V1 =V1 +V1 ,V2 =V2 +V2 ,I1 = − ,I 2 = − Z 0 Z 0 Z 0 Z 0 b  S S a  b V − 1 = 11 12 1 = i = i     ,S ij + b2  S 21 S 22 a2  a j V j + ai =0,k ≠ j V k =0,k ≠ j

1 * 1 2 1 2 Incident power to port i: P = ℜe{ V I }= a − b i 2 i i 2 i 2 i

Massachusetts Institute of Technology RF Cavities and Components for Accelerators USPAS 2010 26 Properties of S- Parameters b S = 1 : reflection coefficient at port 1 with port 2 matched 11 a 1 a2 =0 b S = 2 : forward transmission coefficient with port 2 matched 21 a 1 a2 =0

b S = 1 12 a : reversed transmission coefficient with port 1 matched 2 a1 =0 b S = 2 22 a : reflection coefficient at port 2 with port 1 matched 2 a1 =0

2 IL or power gain from port 1 to port 2 = −10log S 21 2 IL or power gain from port 2 to port 1 = −10log S12 2 2 RL at port 1 or port 2 = − 10 log S 11 or = −10log S 22

Massachusetts Institute of Technology RF Cavities and Components for Accelerators USPAS 2010 27 Properties of S- Parameters

a′ a1 S21 b2 b′ l 1 2 1 [S ] l2 • • • • S11 S • • • • 22 Z0 [S] Z0 b′ a′ • • • • 1 • b• S • • 2 1 12 a2

− j 2βl1 − j 2β(l1 +l2 ) S11′ = S11e ,S 21′ = S 21e b1 = a1S11 + a2S12 − j 2β(l1 +l2 ) − j 2βl2 S12′ = S12e ,S 22′ = S 22e b2 = a1S 21 + a2S 22

Reasons to use S-matrix in microwave circuit

(1) matched load available in broadband application (2) measurable quantity in terms of incident, reflected and transmitted waves (3) termination with Z0 causes no oscillation (4) convenient to use in the microwave network analysis

Massachusetts Institute of Technology RF Cavities and Components for Accelerators USPAS 2010 28 Microwave analyzers Spectrum analyzer

Purpose: measure microwave signal spectrum, can also be used to measure frequency, rms voltage, power, distortion, noise power, amplitude modulation, frequency modulation, spectral purity,...

Operating principle

Mixer IF Amp  Log/Lin Adjust  Amp Detector Bandwidth

Y X Horizontal Swept LO Sweep CRT Generator Amp Scan width Center frequency Scan time

Massachusetts Institute of Technology RF Cavities and Components for Accelerators USPAS 2010 29 Network analyzer

Purpose: measure two-port S-parameter of a microwave device or network, can also be used to measure VSWR, return loss, group delay, input impedance, antenna pattern, dielectric constant,….

Operating principle

Massachusetts Institute of Technology RF Cavities and Components for Accelerators USPAS 2010 30 Scalar network analyzer measures the magnitude of two-port S- parameters.

Hp8510 vector network analyzer

Massachusetts Institute of Technology RF Cavities and Components for Accelerators USPAS 2010 31