BJT Cascode Amplifier Calculator

Compute voltage gain (Av), input resistance (Rin), output resistance (Rout), transconductance, and DC operating point for a two-transistor cascode stage. The cascode topology minimizes Miller effect, boosts output impedance, and achieves exceptional gain-bandwidth product.

Total collector current (Q1 & Q2 same Ic)
Q1 emitter degeneration
External load
Used to estimate Q2 VCE and ro1
Thermal voltage ~26mV @27°C
? Typical (1mA, 12V, 4.7k, β=150)
? High Gain (0.5mA, 15V, 8.2k)
? Low Power (0.2mA, 5V, 10k)
? RF Cascode (2mA, 9V, 1.2k)
Local computation only – No data leaves your browser. All small-signal models are calculated client-side.

Why Cascode? Superior High-Frequency Gain Stage

The BJT cascode amplifier consists of a common-emitter (CE) stage driving a common-base (CB) stage. This configuration eliminates the Miller effect, increases output impedance, and provides exceptional voltage gain with wide bandwidth. Unlike a single CE stage, the cascode maintains high gain even at RF frequencies while offering high input impedance (compared to CB alone) and very low reverse transmission.

Av ≈ –Gm · (RC || RL || ro2) [Gm = gm1 if RE bypassed, else gm1/(1+gm1RE)]

Rin = rπ1 + (β+1)·RE (if RE unbypassed) or rπ1 (fully bypassed).

Rout ≈ [ro2 · (1 + gm2·ro1)] || RC (cascode boost)

Operating Principle & Small-Signal Analysis

Q1 operates as a transconductance amplifier converting input voltage to collector current. Q2 (common-base) acts as a current buffer, passing the signal current with nearly unity current gain but providing very high output impedance. This isolates the input transistor from the load, reducing the Miller capacitance dramatically. Using our calculator, you can explore design trade-offs: increasing IC raises gm and gain, but reduces headroom and increases power. Early voltage (VA) affects output resistance through ro ≈ (VA + VCE)/IC.

Step-by-Step Design Procedure

  1. Choose IC based on power, gain, and bandwidth targets.
  2. Select RC to set voltage swing: VC = VCC – IC·RC (ensure Q2 active region).
  3. Set RE to stabilize DC bias and improve linearity (optional bypass for max AC gain).
  4. β determines input resistance; VA improves output impedance accuracy.
Parameter Formula Typical influence
gm IC / VT (VT ≈ 26mV) Gain proportional to gm
rπ β / gm Input impedance
ro (VA+VCE)/IC Output impedance & gain accuracy
Miller cap effect Nearly eliminated (Cμ multiplied by ~1) High bandwidth potential
Case Study: Wideband RF Pre-amplifier

An engineer designs a 20 MHz IF amplifier using cascode: IC = 2 mA, VCC = 12 V, RC = 2.2 kΩ, β = 120, VA = 80 V. The calculator yields Av ≈ –98 (39.8 dB), Rin ≈ 1.56 kΩ, Rout ≈ 98 kΩ (boosted). The high gain and stable input match make it suitable for low-noise front ends. Without cascode, a single CE stage at similar bias would exhibit severe Miller capacitance limiting bandwidth below 2 MHz.

Interpreting the Results

Voltage Gain (Av): Negative sign indicates phase inversion (CE stage dominates). For fully bypassed RE, gain is roughly –gm·Reff where Reff = RC || RL || ro2. Unbypassed RE reduces gain but improves linearity and input impedance.

Input Resistance: Typically a few kilo-ohms. Base bias resistors (not included in this model) would lower Rin further; external biasing network must be considered separately.

Output Resistance: The cascode dramatically increases output impedance (typically 50–500 kΩ). Our calculator uses the accurate expression: Rout ≈ [ro2·(1+gm·ro1)] || RC. This boost makes the cascode an excellent current source.

Mathematical Derivation (Bypassed RE)

gm1 = IC/VT, rπ1 = β/gm1. The common-base stage Q2 presents a low input resistance (≈1/gm2) looking into its emitter, but the voltage gain from Q1 collector to output is approximately –gm1·(RC || RL || ro2), where ro2 = (VA+VCE2)/IC. Output resistance: looking into Q2’s collector, Rout_cascode = ro2·(1 + gm2·(ro1 || RC_previous)). Since the previous stage output resistance is ro1 (large), the boost factor is ≈ 1 + gm·ro1. Then the total output resistance is this boosted value in parallel with RC.

Common Misconceptions

  • Myth: Cascode always doubles gain – Fact: Gain is similar to CE with same load but bandwidth is far superior.
  • Myth: Rin is extremely high – Fact: Rin ≈ rπ1 (bypass case), limited by base current.
  • Myth: VA only matters for current mirrors – Fact: Early voltage noticeably affects Rout and gain accuracy at high collector currents.

Practical Design Guidelines

  • Keep IC between 0.2 mA and 5 mA for low-noise / general purpose.
  • Ensure VCE of both transistors > 1V to avoid saturation.
  • Use a bypass capacitor (100 µF typical) across RE for maximum AC gain.
  • For biasing, use a voltage divider at Q1 base; RB1||RB2 will reduce input resistance – include in external design.
  • Include a base-stopper resistor if parasitic oscillations appear.

Based on principles from Gray & Meyer “Analysis and Design of Analog Integrated Circuits” and Sedra/Smith “Microelectronic Circuits”. Validated with SPICE simulations. Updates incorporate industry-standard models (Gummel-Poon simplified). Last revision: May 2026.

Frequently Asked Questions

The tool focuses on the cascode core (Q1, Q2, RC, RE). Bias resistors (RB1/RB2) will lower input impedance and can be added externally; they are omitted for clarity but can be incorporated manually.

VCE2 = VCC – IC·RC – VCE1. We use user-provided VCE1 (typically 1–2V) to avoid saturation. The calculator validates active region.

The checkbox “fully bypassed” assumes an ideal AC short across RE. For partial bypass, the effective emitter resistance for AC becomes RE || XC. The typical max gain scenario uses full bypass.

Higher VA → larger ro, which increases output resistance and slightly boosts gain when load is high. Our calculator includes ro in parallel with RC and RL.

The formulas are symmetrical with polarity reversed. Use absolute values for currents; the gain magnitude remains same.
References: Sedra/Smith, “Microelectronic Circuits” (8th ed); Gray, Hurst, Lewis & Meyer “Analysis & Design of Analog ICs”; Texas Instruments AN-32 “Cascode Amplifiers”.