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~ Common Emitter Amplifier Gain & Noise Calculator ~

 

CE amplifier Noise model

Calculates the root mean square Noise Voltages VN(rms) at the OUTPUT of a single stage Common Emitter amplifier based on the a.c. model opposite and input variables entered ~ The focus is on the amplifier Noise Figure [NF] and Signal to Noise Ratio [SNR] for a given input signal VS ~ Additional results in nV/√Hz are the respective noise voltages in a 1Hz bandwidth 

It does not take into account flicker noise and assumes perfect resistive loads and modern silicon transistors with low noise bias and the transistor gain [β] remains constant within the measurement bandwidth [Bn] defined

The circled nodes B C and E represent the external connections of the transistor and lower case rbb and re are internal but also in series with B and E respectively ~ Collector or output resistance ro is not used here but can be added parallel with RC and will reduce the gain along with the output noise

Simply referring only the transistor noise to the input does not give the full picture for a common emitter or common base amplifier where base and collector shot noise cancellation can occur ~ Also some of the formulae found in even the best reference and often repeated assume that β ≫ 1 and re ≥ rbb which for low source resistance designs is not always the case ~ Click here for other calculators

There are a lot of outputs and although this looks confusing at first it is advantageous to have all these intermediate answers readily available and gives an insight to what effect the input changes have on the gain and input impedance and noise from each source ~ Start by entering your Collector Current

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 [ adjust for load resistor and ro if known ]
Emitter Resistor —RE Ω [ un-decoupled emitter resistor ]
Source Resistor — RS Ω [ you need RS to have a Noise Figure ]
Intrinsic Base Resistance — rbb Ω [ or rbb' resistance of the base material ]
Transistor d.c. current gain — β [ hFE or "beta" in some texts ]
Collector Current — IC mA
Device Temperature — T ˚C [ calculation uses ˚K ]
Measurement Noise Bandwidth — Bn Hz — Is not the −3dB BW see Here
Calculated results using input variables above
Signal VS — SNRout dB = 20 log GVVS/VNtot [ Otput SNR for VS entered ]
SNR due to RS & RE dB = 20 log VS/√4 k T Bn (RS+RE)
SNR due to RS alone — SNRin dB = 20 log VS/√4 k T Bn RS
Amplifier Noise Figure — NF dB = SNRin – SNRout
Amplifier Voltage Gain — GV V/V = Rin/(RS+Rin) · α RC/(rbb /(1+β)+re+RE)
Amplifier input impedance — Rin kΩ= RB ∥(rbb+(1+β) (re+RE))
Amplifier output Voltage — Vout mVrms =  GV · VS    = dBV
Emitter Internal Resistance — re Ω = VT/IC   VT = kT/q = mV
Common base current gain — α = IC/(IC+IB)  IB = IC/β= µA
Internal Voltage Gain — AV V/V = α RC/(re+RE)   [ gain after rbb ]
Noise at Collector due to RS — VNRS µVrms = √4 k T Bn RS · AV nV/√Hz
Noise at Collector due to rbb — VNrbb µVrms = √4 k T Bn rbb · AV 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 = √2q IB Bn · (rbb+RS∥RB−re−RE) · AV
Noise at collector due to IC — VNIC µVrms = √2q IC Bn · (RC−re−RE)
Total Noise at Collector — VNtot

µVrms=√NRS+V²Nrbb+V²NRE+V²NRC+V²NIB+V²NIC

Transistor only calculations from references below Using input values from above
Noise Resistor in series at Base — RNV Ω = rbb+ re/2  √4 k T RNV =  nV/√Hz
Noise Resistor Base to Emitter — RNI kΩ = 2 β re    √4 k T/ RNI  =  pA/√Hz
Optimum Source R — RS(opt) Ω = √RNV RNI
Noise Figure for RS(opt) — NF(opt) dB = 10 log (1 +(2 √RNV /RNI))
Optimum Collector Current — ICopt mA = β/√1+β · VT/(rbb+RS+RE)
NF using input values of IC and RS dB = 10 log 1+(rbb+re/2)/RS+(rbb+re+RS)2/2β reRS

Nota Bene See these references:

The Art of Electronics 3rd edition chapter 8 ~ By Paul Horowitz and Winfield Hill

Noise in Transistor Circuits ~ By P. J. Baxandall ~ Wireless World November 1968

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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