Cascading Stages

Part of Vacuum Tubes

Cascading amplifier stages multiplies gain and enables the signal processing chain needed for radio receivers, audio amplifiers, and transmitter modulators.

Why This Matters

A single amplifier stage provides limited gain — typically 10 to 100 times for a triode, up to a few hundred for a pentode. A microphone produces millivolt-level signals. A speaker needs volt-level signals. A radio receiver’s antenna captures microvolt signals that must reach millivolt levels to drive a detector. Getting from source to destination requires multiple stages in series, each multiplying the signal, with the gains of all stages multiplied together.

Understanding how to cascade stages correctly is the core skill of vacuum tube circuit design. The individual stage design — bias point, plate resistor, cathode bypass — is important, but the interaction between stages introduces new problems: the loading of one stage by the next reduces gain; coupling capacitors create frequency response limits; power supply coupling between stages can cause oscillation; and each stage adds noise that accumulates through the chain.

Community communication systems — radio transmitters, receivers, public address amplifiers, telephone repeaters — all depend on properly cascaded amplifier stages. Getting the cascade right from the start, rather than troubleshooting a misbehaving multi-stage chain, requires understanding these interactions before connecting the stages together.

Stage Gain and Loading Effects

When two stages are connected, the input impedance of the second stage loads the plate resistor of the first stage. The effective load seen by the first tube is no longer just the plate resistor but the parallel combination of the plate resistor and the second stage’s input impedance.

For a resistively coupled triode stage, the second stage’s input impedance is the grid resistor (typically 470 kilohms to 1 megohm). If the first stage has a 100 kilohm plate resistor, the effective load is:

Reff = (100k × 1M) / (100k + 1M) = 91 kilohms

This is close to the unloaded value because the grid resistor is much larger than the plate resistor. But if you increase the plate resistor to 1 megohm seeking higher gain, the effective load drops to:

Reff = (1M × 1M) / (1M + 1M) = 500 kilohms

The gain increase from doubling the plate resistor is partially offset by the loading. As a practical rule, choose the plate resistor no larger than about one-third of the following stage’s grid resistor for acceptable loading.

For pentode stages, the issue is more complex because pentodes have very high plate resistance (hundreds of kilohms to several megohms). The plate resistance acts in parallel with the plate resistor and the next stage’s grid resistor. With a pentode’s high plate resistance, the gain is primarily determined by transconductance times load impedance, and loading effects are similar to the triode case.

Coupling Methods in Cascades

The choice of coupling method between stages affects frequency response, noise, component count, and design complexity.

RC coupling is almost universal in audio and low-frequency amplifiers. Each coupling capacitor forms a high-pass filter with the following stage’s grid resistor. The lower -3dB frequency is 1/(2π × Rg × Cc), where Rg is the grid resistor and Cc is the coupling capacitor. For flat response down to 20 Hz with a 1-megohm grid resistor, Cc must be at least 8 microfarads. Electrolytic capacitors in this range are common in salvage.

Multiple RC coupling stages each contribute a lower frequency rolloff. Three stages each with a 20 Hz cutoff produce a combined rolloff that starts at a higher frequency than 20 Hz. For a system needing flat response to 20 Hz, design each stage’s coupling to cut off at 5-7 Hz to allow margin for the combined effect.

At high frequencies, the stray capacitance of wiring, tube sockets, and component leads forms a low-pass filter. Each grid-to-cathode capacitance shunts the plate resistor, causing the gain to roll off above a cutoff frequency. In audio amplifiers this typically occurs above 20-50 kHz, well beyond audible range. In RF and IF amplifiers it is a critical constraint.

Transformer coupling between stages provides impedance transformation and can improve gain efficiency when source and load impedances would be mismatched in a resistive coupling. An interstage transformer wound for a step-up ratio boosts voltage gain without requiring a higher supply voltage. The transformer’s frequency response limits are the bandwidth limit; a well-made audio interstage transformer typically covers 50 Hz to 20 kHz. Transformer coupling was standard in early radio designs before large-value coupling capacitors became available.

Power Supply Decoupling

A cascaded amplifier chain shares a single power supply. Each stage draws varying current as it processes a signal. These varying currents flow through the supply’s internal resistance and filter components, creating small voltage variations on the supply rail. These variations appear as a signal fed into every stage connected to the same rail — creating a feedback path that can cause the amplifier to oscillate or to have poor low-frequency response.

Decoupling each stage prevents this interaction. Between the main supply and each stage’s plate resistor, insert a decoupling resistor (typically 10 to 47 kilohms) and a decoupling capacitor (47 to 100 microfarads) to ground. This low-pass filter allows DC from the supply to reach the stage but blocks AC variations on the supply rail.

The decoupling resistor causes a voltage drop equal to the stage current times the resistance. Account for this when calculating the supply voltage needed. A stage running at 1mA through a 10 kilohm decoupling resistor drops 10V, requiring the main supply to be 10V higher than the desired plate voltage.

In a three-stage amplifier with stages labeled 1 (output), 2 (driver), and 3 (input), the decoupling time constants should be largest at the output stage and smallest at the input stage. This ensures that low-frequency signals from the output do not couple back to the high-gain input through supply variations. If the output stage momentarily pulls more current, the decoupling filter for stages 2 and 3 prevents this from disturbing their supply voltage.

Practical Design of a Three-Stage Audio Chain

A common configuration for a community PA system or radio station monitor amplifier uses a three-stage chain: input preamplifier (high-mu triode), driver (medium-mu triode), and output (beam power pair in push-pull).

Stage 1: 12AX7 common cathode, plate resistor 100k, cathode resistor 1.5k with 10µF bypass, coupling capacitor 0.1µF, grid resistor 1M. Supply: 250V. Expected gain: approximately 55.

Stage 2: 12AU7 common cathode acting as both amplifier and phase splitter. One plate resistor feeds the first output tube grid; a second identical resistor from the cathode resistance provides an inverted phase for the second output tube grid. This “cathodyne” phase splitter produces equal and opposite signals with gain slightly less than unity.

Stage 3: Two 6L6 tubes in Class AB push-pull. Grid bias from cathode resistors. Output transformer with primary center tap connected to B+ supply, plate leads to each tube’s plate. Secondary connected to speaker.

Total voltage gain from microphone to speaker input: approximately 40 times (stage 1 gain of 55, reduced by loading and the phase splitter gain below unity). With a typical microphone output of 5mV, the output stage receives roughly 200mV — adequate to drive the 6L6 tubes to near full output. If more gain is needed, add a second 12AX7 stage between stages 1 and 2 for a factor-of-50 increase.

Layout is critical in multi-stage amplifiers. Keep input and output leads physically separated. Run input wiring as far as possible from output wiring and from the power transformer. Ground all shield cans and ground the chassis at a single point rather than at each stage. A “star grounding” topology where all ground returns meet at a single point prevents ground loops that create hum.