Noise Figure Measurements
Feb 24, 2009 Account Manager : Peter Caputo Presented by : Ernie Jackson Agenda • Overview of Noise Figure • Noise Figure Measurement Techniques • Accuracy Limitations • PNA-X’s Unique Approach
Gain
So/N o DUT
Si/N i
Noise Figure Basics Page 2 Noise Contributors
Thermal Noise: (otherwise known as Johnson noise) is the kinetic energy of a body of particles as a result of its finite temperature
Ptherm =kTB
Shot Noise: caused by the quantized and random nature of current flow
Flicker Noise: (or 1/f noise) is a low frequency phenomenon where the noise power follows a 1/f ααα characteristic
Noise Figure Basics Page 3 Why do we measure Noise Figure? Example...
Transmitter: ERP = ERP + 55 dBm +55 dBm Path Losses -200 dB Rx Ant. Gain 60 dB dB Power to Rx -85 dBm -200 ses: Los Receiver: Path
Noise Floor@290K -174 dBm/Hz C/N= 4 dB Noise in 100 MHz BW +80 dB Receiver NF +5 dB Rx Sensitivity -89 dBm
Choices to increase Margin by 3dB Receiver NF: 5dB 1. Double transmitter power Bandwidth: 100MHz Power to Antenna: +40dBm 2. Increase gain of antennas by 3dB Antenna Gain: +60dB Frequency: 12GHz 3. Lower the receiver noise figure by 3dB Antenna Gain: +15dB
Noise Figure Basics Page 4 The Definition of Noise Factor or Noise Figure in Linear Terms
• Noise Factor is a figure of merit that relates the Signal to Noise ratio of the output to the Signal to Noise ratio of the input. • Most basic definition was defined by Friis in the 1940’s. S S S N N in out N F = in S G , Na N out
Reference: Harald Trap Friis: 1944: Proceedings of the IRE
Noise Figure Basics Page 5 What is Noise Figure ?
Noise Out Noise in
Measurement bandwidth=25MHz a) C/N at amplifier input b) C/N at amplifier output Nin Nout
Noise Figure Basics Page 6 Definition of Noise Figure
S S Nout N in N out Noise N a Added
G , Na GNin
Sout f1 f2 Gain = G = Nout = Na + GNin Sin N + GN S Nout a in F = = Noise Factor N GNin GNin F = in S N + GN NF (dB) =10log a in N Noise Figure out GNin
Noise Figure Basics Page 7 Noise Voltage
Standard Equation for Noise Voltage produced by a Resistor
e2 = 4kTBR
k = Boltzman's Constant = .1 38×10−23 Joules/°K is T is absolute temperature ( °K) is B is bandwidth (Hz) e is rms voltage
Reference: JB Johnson/Nyquist: 1928: Bell Labs
Noise Figure Basics Page 8 Noise Power at Standard Temperature
Thermal Load k = 1.38 x 10 23 joule / k R - j X T = Temperature (K) R+jX L L B = Bandwidth (Hz)
Available Noise Power Delivered to a Conjugate Load,
Pav = kTB
-21 At 290K P av = 4 x 10 W/Hz = -174dBm / Hz
In deep space kT = -198dBm/Hz
Noise Figure Basics Page 9 Noise Power is Linear with Temperature
Nin Nout = Na + GNin
= Na + GkTs B G , Na Z s @ Ts
Nout Slope = kGB N2
N1
Na Output Noise Noise Output Power Ts T1 T2 Temperature of Source Impedance
Noise Figure Basics Page 10 An Alternative Way to Describe Noise Figure:
Effective Input Noise Temperature ( T e)
N = N + GN ∑∑∑ out a in = GkTe B + GkTs B G , Na = 0 = GkB(Te +Ts ) Z s @ Ts Z s @ Te N out Slope = kGB
T = (F −1)T e s N
and a Output Noise Noise Output Power
Ts Te +Ts TemperatureT of Source F = e Impedance Ts Noise Figure Basics Page 11 Te or NF: which should I use?
••UseUse either either - - they they are are completely completely interchangeable interchangeable ••TypicallyTypically NF NF for for terrestrial terrestrial and and Te Te for for space space ••NFNF referenced referenced to to 290K 290K - - not not appropriate appropriate in in space space ••IfIf Te Te used used in in terrestrial terrestrial systems, systems, the the temperatures temperatures cancan be be large large (10dB=2610K) (10dB=2610K) ••TeTe is is easier easier to to characterize characterize graphically graphically
Noise Figure Basics Page 12 Friis or Cascade Equation
• Here we see what contribution a second amplifier has on the overall noise factor.
N = N + G N + G G N Nin out a2 1 a1 1 2 in
G = G1G2 G , N G , N 1 a1 2 a2 Nin = kTs B Z s @ Ts Na1 = kTe1B = (F1 −1)kTs B
Na2 Na2 = kTe2 B = (F2 −1)kTs B N F = out
Na1G2 GNin Na1
kT B kT BG kT BG G F2 −1 Nin = s s 1 s 1 2 F12 = F1 + G1
Noise Figure Basics Page 13 Effects of Multiple Stages on Noise Factor
• The cascade equation can be generalized for multiple stages
Nin
G1 , Na1 G2 , Na2 GN , N N 2 Z s @ Ts F −1 F −1 F = F + 2 +L+ N total 1 K G1 G1G2 GN −1 N F −1 F = F + i total 1 ∑ N i=2 G ∏ j−1 j=i
Noise Figure Basics Page 14 Demo of Cascade Equation F2 −1 F = F1 + G1
ABC
Gain (dB) 6.0 12.0 20.0 Gain 4.0 16.0 100.0 Noise Figure(dB) 2.3 3.0 6.0 Noise Factor 1.7 2.0 4.0
0.2 −1 0.4 −1 F = 7.1 + + = .1 70 + .0 25 + .0 047 = .1 997 ABC 4.0 4.0×16.0 NFABC =10log( .1 997) = .3 00 dB 0.4 −1 0.2 −1 F = 7.1 + + = .1 70 + .0 75 + .0 025 = .2 475 ACB 4.0 4.0×100.0 NFACB =10log( .2 475) = .3 93 dB
Noise Figure Basics Page 15 Agenda • Overview of Noise Figure • Noise Figure Measurement Techniques • Accuracy Limitations • PNA-X’s Unique Approach
Gain
So/N o DUT
Si/N i
Noise Figure Basics Page 16 Measuring Noise Figure
Na + Nin .Ga F = Nin . Ga Nin Nout = Na + kTB Ga
Rs Ga , Na
r e
w Slope=kBGa
o
P