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~ Common Emitter Amplifier Noise Calculator ~

Calculates the root mean square value of the Noise Voltages VN(rms) that appear at the OUTPUT of a single stage Common Emitter (CE) amplifier based on the a.c. model opposite

The focus is on the amplfier Noise Figure ~ Resuts in nV/√Hz are the respective resistor Johnson noise voltages

It does not take into account flicker noise and assumes: Perfect resistive loads and modern silicon transistor with low noise bias and the transistor gain (β) is constant within the measurment bandwidth (Bn) defined

The circled nodes B C and E represent the external connections of the transistor so rbb and re are internal ~ output resistance ro is not used here

 

Boltzmann Constant — k
1.3806x10-23
 J/K ( joules/kelvin )
Charge on a single Electron — q
1.6022x10-19
C ( coulomb or amperes/sec )
Base bias Resistor — RB
Ω ( Base bias total resistance )
Collector Resistor — RC
Ω ( load resistor )
Emitter Resistor —RE
Ω ( undecoupled emitter resistor )
Source Resistor — RS
Ω  
Intrinsic Base Resistance — rbb
Ω ( resistance of the base material )
Transistor d.c. current gain —β
   ( also hFE or 'beta' in some texts )
Collector Current — IC
mA  
Device Temperature — T
˚C ( calculation uses ˚K )
Measurement Noise Bandwidth — Bn
Hz
Calculated results using the values entered above
Signal   VS — SNR
dB = 20 log (GVVS/VNtot)       (SNRout)
Maximum SNR due to RS & RE
dB = 20 log (VS/√4 k T Bn (RS +RE)  )
Maximum SNR due to RS alone
dB = 20 log (VS/√4 k T Bn RS)    (SNRin)
Noise Figure NF
dB = SNRout –SNRin
Emitter Internal Resistance — re
Ω = VT/IC       VT = kT/q = mV
Common base current gain —α
= IC/(IC + IB)   IB = IC/β = µA
Amplifier input impedance — Rin
=  RB ‖ (rbb + (1 + β) (re + RE))
Voltage Gain — Av
V/V = α RC/(re + RE)
Amplifier Voltage Gain — Gv
V/V = AV Rin /(RS + Rin) = dB
Noise at Collector due to RS — VNRS
µVrms = √4 k T Bn RS  •Gv    nV/√Hz
Noise at Collector due to rbb — VNrbb
µVrms = √4 k T Bn rbb  •Gv    nV/√Hz
Noise at Collector due to RE — VNRE
µVrms = √4 k T Bn RE  •Av    nV/√Hz
Noise at Collector due to RC — VNRC
µVrms = √4 k T Bn RC            nV/√Hz
Noise at collector due to IB — VNIB
µVrms = √2 q IB B (rbb + RS‖R) •Gv
Noise at collector due to IC — VNIC
µVrms = √2 q IBn  (R– (re + RE))
Total Noise V at Collector — VNtot
µVrms = √VNRS2+VNrbb2+VNRE2+VNRC2+VNIB2+VNIC2
     
Transistor only noise sources referred to input as series and parallel noise resistances RNV and RNI
Noise Resistor in series at Base — RNV
Ω = rbb + re/2
Noise Resistor Base to Emitter — RNI
Ω = 2 β re
Optimum Source Resistance — RS(opt)
Ω = √RNV RNI
Optimum Collector Current — IC(opt)
mA = β/√1 + β  • VT/(rbb + RS + RE)
   

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See these references:

The Art of Electronics 3rd edition chapter 8 ~ By Paul Horowitz and Winfield Hill ~ fellow cynics
Noise in Transistor Circuits ~ By P. J. Baxandall ~ Wireless World November 1968 ~ often referenced
Designing low–noise audio amplifiers ~ By Wilfried Adam ~ Wireless World June 1989
Introduction to low–noise amplifier design ~ By A. Foord ~ Wireless World April 1981
The design of Low-noise audio frequency amplifiers ~ By E. A. Faulkner ~ The Radio and Electronic Engineer July 1968 ~ This article along with the book 'Low-Noise Electronic System Design' By C. D. Motchenbacher and J. A. Connelly should answer most questions about electronic noise


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