BJT cascode amplifier small-signal analysis
A BJT cascode combines a common-emitter input device with a common-base device. The arrangement suppresses the Miller effect and raises output resistance, which can improve gain-bandwidth behavior.
This calculator applies a simplified room-temperature hybrid-pi estimate. It is suitable for first-pass analysis; a real circuit also depends on bias networks, device capacitances, source resistance, loading, process spread, and operating-point limits.
How to use the BJT cascode amplifier calculator
- Enter the operating point: Provide supply voltage, collector current, current gain, and Early voltage.
- Enter loading: Provide collector and load resistances plus input and output capacitances.
- Analyze: Generate gain, impedance, cutoff-frequency, and power estimates.
- Check the circuit: Verify voltage headroom, transistor ratings, bias loading, stability, and parasitics with a circuit model.
Formula and variables
Transconductance is estimated from collector current and thermal voltage. Loaded gain uses the parallel collector, load, and cascode output resistances.
gₘ = I꜀/Vₜ; Aᵥ ≈ gₘ(R꜀ ∥ Rₗ ∥ rₒ,cascode)- I꜀ — Collector current
- DC operating collector current (A)
- Vₜ — Thermal voltage
- Approximately 25.85 mV at room temperature (V)
- R꜀ — Collector resistor
- External collector resistance (Ω)
- Rₗ — Load resistance
- External output load (Ω)
- Vₐ — Early voltage
- Parameter used to estimate transistor output resistance (V)
One-milliamp cascode example
A 12 V cascode operates at 1 mA with β = 100, R꜀ = 3.3 kΩ, Rₗ = 10 kΩ, and Early voltage 100 V.
- Supply and current
- 12 V, 1 mA
- Resistors
- 3.3 kΩ and 10 kΩ
- Early voltage
- 100 V
- gₘ = 0.001/0.02585 ≈ 38.68 mS
- rₒ ≈ 100/0.001 = 100 kΩ
- Gain uses gₘ multiplied by the loaded parallel resistance
Result: The calculator reports the resulting midband gain and related small-signal metrics.
External collector and load resistors often limit practical gain even when cascode output resistance is high.
Understanding your results
Using the estimates
Treat gain magnitude as a small-signal midband estimate rather than guaranteed closed-loop performance.
- Upper cutoff uses the entered output capacitance and loaded resistance.
- The power value is a simplified two-device DC estimate.
- Input impedance follows the simplified β/gₘ relationship used by this model.
Assumptions
- Both transistors remain in forward-active operation.
- Room-temperature thermal voltage and matched operating current.
- Small-signal linear operation with simplified capacitances.
Limitations
- Does not solve the bias network, voltage swing, noise, distortion, stability, or device breakdown constraints.
- Does not replace SPICE simulation or measured transistor parameters.
Common mistakes
- Entering milliamps as amps or kilohms as ohms.
- Ignoring the headroom required by stacked transistors.
- Assuming β and Early voltage are constant across devices and current.
- Treating calculated gain as valid at every frequency.
Practical use cases
First-pass analog design
Compare resistor, current, load, and capacitance choices before detailed simulation.
Cascode education
Study why high output resistance and reduced Miller multiplication can improve amplifier performance.
Frequently asked questions
Why does a cascode improve bandwidth?
The common-base device holds the input transistor collector at a relatively small signal variation, reducing Miller multiplication of collector-base capacitance.
Why can calculated gain be too high?
Bias-network loading, finite device parameters, source resistance, parasitics, output swing, and frequency effects reduce practical gain.
Does the calculator check transistor ratings?
No. Verify current, voltage, power dissipation, safe operating area, and thermal limits separately.
Sources and review
- Microelectronic Circuits — Oxford University Press. Accessed 2026-07-13.
- The Art of Electronics — Cambridge University Press. Accessed 2026-07-13.
Reviewed 2026-07-13.