Cascode Amplifier

A cascode amplifier stacks a common-emitter stage directly below a common-base stage. RF front-ends in FM receivers and wideband oscilloscopes use this arrangement to achieve high gain without the bandwidth loss that plagues a single high-gain stage.

Core Concept

The main weakness of a high-gain common-emitter amplifier is the Miller effect. The collector-base capacitance Cμ gets multiplied by (1 + Av) and appears as a large capacitor at the input. At high frequencies, this capacitor shunts the input signal to ground and destroys bandwidth.

The cascode solves this by keeping Q1 (CE stage) at a low voltage gain of approximately 1. The common-base Q2 stage provides high output impedance and delivers the voltage gain. Because Q1 sees almost no voltage swing at its collector, Cμ of Q1 is not multiplied. The full gain still appears at Vout.

The result is a bandwidth that can be 10 to 100 times wider than a single CE amplifier with the same DC gain. The cascode is found in LNA (low-noise amplifier) designs in chips like the AD8099 and in discrete RF stages using 2N5179 or BFR93 transistors.

Key Equations

Voltage gain of cascode (same as CE alone): Av = -gm × RC

Transconductance: gm = IC / VT where VT = 26 mV at 300K and IC is the quiescent collector current.

Input capacitance of Q1 (Miller suppressed): Cin ≈ Cπ + Cμ × (1 + gm/gm2) ≈ Cπ + 2Cμ instead of Cπ + (1 + Av)Cμ.

Unity-gain bandwidth: fT = gm / (2π × (Cπ + Cμ))

Output impedance of cascode: Rout ≈ β × ro2 which is very high, making the cascode a near-ideal current source.

Given:
  VCC = 15V
  RC = 2.2 kΩ
  IC = 2 mA (quiescent)
  VT = 26 mV
  Cμ = 4 pF (2N3904 spec)
  Single CE Av = -gm × RC (for comparison)

Why this formula:
  gm controls gain; suppressed Miller capacitance defines bandwidth.

Formula:
  gm = IC / VT
  Av = -gm × RC
  Miller Cap (CE alone) = Cμ × (1 + |Av|)
  Miller Cap (Cascode)  ≈ 2 × Cμ

Substitution:
  gm = 2×10⁻³ / 26×10⁻³ = 0.0769 S = 76.9 mA/V
  Av = -76.9×10⁻³ × 2200 = -169

Calculation:
  Miller Cap CE alone = 4 pF × (1 + 169) = 680 pF
  Miller Cap Cascode  = 4 pF × 2       =   8 pF

  Bandwidth improvement factor ≈ 680 / 8 = 85×

Final Answer:
  gm = 76.9 mA/V
  Av = -169 (same for both topologies)
  Miller capacitance reduced from 680 pF to 8 pF
  Bandwidth improves approximately 85 times

Exam Tip: GATE asks why cascode improves bandwidth. The answer is Miller effect suppression, not that gm changes. The gain formula Av = -gm×RC is identical to a single CE stage. Students often write a different gain formula for the cascode; this is wrong. Also remember: the CB stage presents a low input impedance to Q1's collector, so Q1 has a voltage gain of roughly -1, keeping its Miller cap small.

Key Properties

• Voltage gain equals that of a single CE stage: Av = -gm × RC. The cascode does not increase DC gain.
• Miller input capacitance is reduced from (1+Av)×Cμ to approximately 2×Cμ, dramatically extending bandwidth.
• Output impedance is very high (≈ β × ro), making the cascode an excellent current source in op-amp output stages.
• Requires a higher supply voltage than a single CE stage because two VCE_sat drops must be accommodated.
• The bias voltage on the Q2 base (cascode node) is held constant by a stiff voltage divider or a separate bias IC. It is an AC ground.
• FET versions (NMOS cascode) are common in op-amp input stages; the principle is identical to the BJT version.
• Used in low-noise amplifiers (LNAs) for 50Ω RF systems where simultaneous noise matching and gain are needed.

Quick Revision

• Cascode = CE stage (Q1) + CB stage (Q2) stacked vertically.
• Same gain as CE alone: Av = -gm × RC.
• Key benefit: Miller capacitance of Q1 is suppressed from (1+Av)Cμ to ≈ 2Cμ.
• Bandwidth improvement factor ≈ (1 + |Av|) / 2.
• Q2 base is AC grounded through a bypass capacitor.
• Output impedance ≈ β × ro (very high), ideal for current mirror loads.
• Needs higher VCC than a simple CE stage (need VCE_sat for both Q1 and Q2).
• Exam trap: writing that cascode increases voltage gain. It does not. It only extends bandwidth by killing the Miller effect.