~ Common Emitter Amplifier Gain & Noise Calculator ~

Calculates the root mean square Noise Voltages V_N(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 V_S ~ 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 [B_n]defined

The circled nodes B C and E represent the external connections of the transistor and lower case r_bb and r_e are internal but also in series with B and E respectively ~ Collector or output resistance r_o is not used here but can be added parallel with R_C 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 r_e ≥ r_bb 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 — R_B		Ω [ base bias total resistance ]
Collector Resistor — R_C		Ω [ adjust for load resistor and r_o if known ]
Emitter Resistor —R_E		Ω [ un-decoupled emitter resistor ]
Source Resistor — R_S		Ω [ you need R_S to have a Noise Figure ]
Intrinsic Base Resistance — r_bb		Ω [ or r_bb' resistance of the base material ]
Transistor d.c. current gain — β		[ h_FE or "beta" in some texts ]
Collector Current — I_C		mA
Device Temperature — T		˚C [ calculation uses ˚K ]
Measurement Noise Bandwidth — B_n		Hz — Is not the −3dB BW see Here
Calculated results using input variables above
Signal V_S — SNR_out		dB = 20 log G_VV_S/V_Ntot [ Output SNR for V_S entered ]
SNR due only to R_S & R_E		dB = 20 log V_S/√4 k T B_n(R_S+R_E)
SNR due to R_S alone — SNR_in		dB = 20 log V_S/√4 k T B_nR_S
Amplifier Noise Figure — NF		dB = SNR_in – SNR_out
Amplifier Voltage Gain — G_V		V/V= R_in/(R_S+R_in) · α R_C/(r_bb/(1+β)+r_e+R_E)
Amplifier input impedance — R_in		kΩ= R_B ∥(r_bb+(1+β) (r_e+R_E))
Amplifier output Voltage — V_out		mV_rms = G_V · V_S = dBV
Emitter Internal Resistance — r_e		Ω = V_T/I_CV_T= kT/q = mV
Common base current gain — α		= I_C/(I_C+I_B) I_B = I_C/β= µA
Internal Voltage Gain — A_V		V/V= α R_C/(r_e+R_E) [ gain after r_bb]
Noise at Collector due to R_S — V_NRS		µV_rms = √4 k T B_n R_S · A_V nV/√Hz
Noise at Collector due to r_bb — V_Nrbb		µV_rms = √4 k T B_n r_bb · A_V nV/√Hz
Noise at Collector due to R_E — V_NRE		µV_rms = √4 k T B_n R_E · A_V nV/√Hz
Noise at Collector due to R_C — V_NRC		µV_rms = √4 k T B_n R_C nV/√Hz
Noise at collector due to I_B — V_NIB		µV_rms = √2q I_B B_n · (r_bb+R_S∥R_B−r_e−R_E) · A_V
Noise at collector due to I_C — V_NIC		µV_rms = √2q I_C B_n · (R_C−r_e−R_E)
Total Noise at Collector — V_Ntot		µV_rms=√V²_NRS+V²_Nrbb+V²_NRE+V²_NRC+V²_NIB+V²_NIC
Transistor only calculations from references below Using input values from above
Noise Resistor in series at Base — R_NV		Ω = r_bb+ r_e/2 √4 k T R_NV = nV/√Hz
Noise Resistor Base to Emitter — R_NI		kΩ = 2 βr_e √4 k T/ R_NI = pA/√Hz
Optimum Source R — R_S(opt)		Ω = √R_NV R_NI
Noise Figure for R_S(opt) — NF_(opt)		dB = 10 log (1 +(2 √R_NV /R_NI))
Optimum Collector Current — I_Copt		mA = β/√1+β · V_T/(r_bb+R_S+R_E)
NF using input values of I_C and R_S		dB = 10 log 1+(r_bb+r_e/2)/R_S+(r_bb+r_e+R_S)²/2β r_eR_S

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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" Do you work it out one by one ~ Or played in combination "