Differential Voltage Gain Circuit Calculator

Calculator Inputs

Circuit model

Output mode

Non-inverting input V+

Inverting input V-

Transconductance gm, mS

Collector or drain load, Ω

External load, Ω

Emitter/source degeneration, Ω

R1 input resistor, Ω

R2 feedback resistor, Ω

R3 non-inverting resistor, Ω

R4 reference resistor, Ω

CMRR, dB

Gain bandwidth product, MHz

Positive supply, V

Negative supply, V

Output bias point, V

Input impedance, kΩ

Bias current, mA

Formula Used

Differential input: Vid = V+ - V-

Common-mode input: Vcm = (V+ + V-) / 2

Effective load: Reff = RC || RL

Single-ended transistor pair gain: Av = -gm × Reff / [2 × (1 + gm × Re)]

Differential-output transistor pair gain: Av = gm × Reff / (1 + gm × Re)

Resistor differential amplifier gain: Av ≈ average of R2 / R1 and R4 / R3

Output estimate: Vout = Av × Vid + Acm × Vcm

Common-mode gain: Acm = |Av| / 10^(CMRR / 20)

Bandwidth estimate: BW = GBW / |Av|

How to Use This Calculator

Select the circuit model that matches your design.
Enter the non-inverting and inverting input voltages.
For a transistor pair, enter gm, load resistance, external load, and degeneration resistance.
For a resistor amplifier, enter R1, R2, R3, and R4.
Enter CMRR, supply rails, output bias, bandwidth, and impedance values.
Press the calculate button.
Review gain, output, headroom, bandwidth, and power estimates.
Use CSV or PDF buttons to save the calculation result.

Example Data Table

Example	Model	V+	V-	gm or ratio	Load	Expected use
Small sensor pair	Transistor pair	0.020 V	0.005 V	4 mS	10 kΩ	Low signal amplification
Balanced line stage	Resistor amplifier	1.100 V	1.000 V	10 V/V	External stage	Audio or control signal
Degenerated pair	Transistor pair	0.050 V	0.030 V	8 mS	4.7 kΩ	Higher linearity estimate
Instrumentation front end	Resistor amplifier	2.510 V	2.500 V	100 V/V	High impedance	Bridge sensor reading

Differential Voltage Gain Overview

A differential voltage gain circuit compares two input nodes and amplifies only their difference. This behavior is useful in sensor interfaces, audio stages, bridge measurements, instrumentation inputs, and noise resistant links. The calculator supports transistor pair estimates and matched resistor amplifier estimates, so one page can cover many classroom and design checks.

Why Differential Gain Matters

Single ended amplifiers react to one signal referenced to ground. Differential stages react to the voltage between two conductors. Any equal disturbance on both inputs is common mode voltage. A good stage rejects that shared signal while increasing the wanted difference. This improves measurement stability when cables are long, grounds are noisy, or sensor outputs are small.

Design Inputs

The most important values are the two input voltages, the effective load, transconductance, emitter or source degeneration, resistor ratios, and common mode rejection. In a transistor pair, transconductance sets how strongly input voltage changes output current. The collector or drain load turns that current change into voltage. Degeneration resistance reduces gain, but improves linearity and input range.

Result Meaning

The reported differential input is simply the non-inverting input minus the inverting input. The gain is shown as a linear ratio and in decibels. The output estimate is the small signal output caused by the input difference. A separate common mode error is also shown when a CMRR value is entered. This helps compare ideal gain against a more realistic output.

Practical Notes

Use realistic small signal values. Very large differential inputs can push active devices outside the linear region. For resistor amplifiers, matching matters. Equal ratios produce stronger common mode rejection. Even small tolerance errors can create visible output offset. The bandwidth estimate uses a simple gain bandwidth relation, so it is best for first pass planning. Final hardware should still be checked with device data sheets, tolerance analysis, and bench measurements.

Use Cases

Common uses include differential probe scaling, op amp front ends, bridge sensor reading, current shunt sensing, and balanced audio conversion. The tool also helps students see how gain changes when load resistance, degeneration resistance, or resistor ratio shifts. That makes sensitivity checks faster before simulation or layout work begins. It also supports fast worksheet style design comparisons.

FAQs

What is differential voltage gain?

Differential voltage gain is the output voltage change divided by the difference between two input voltages. It shows how strongly a circuit amplifies the wanted differential signal.

What does common-mode voltage mean?

Common-mode voltage is the average voltage present on both inputs. Ideally, a differential circuit rejects it and responds only to the voltage difference.

Why does CMRR matter?

CMRR shows how well the circuit rejects common-mode signals. Higher CMRR reduces unwanted output caused by shared noise or ground shifts.

What is gm in this calculator?

gm means transconductance. It links small input voltage changes to output current changes in a transistor or active differential pair.

What does degeneration resistance do?

Degeneration resistance lowers gain, but it often improves linearity, stability, and usable input range. It is common in practical transistor stages.

Can this replace circuit simulation?

No. It gives a fast first estimate. Use simulation and bench testing for detailed device limits, noise, distortion, temperature effects, and tolerance spread.

How is resistor amplifier gain estimated?

The calculator averages the two resistor ratios. Closely matched ratios improve differential accuracy and reduce common-mode output error.

Why is output headroom shown?

Headroom helps estimate whether the output may clip near the supply rails. Positive margin suggests the small signal estimate fits the available swing.