# Multistage amplifier

Simplified diagram of a 2-stage cascaded amplifier

For many applications, the performance obtainable from a single-stage amplifier is often insufficient, hence several stages may be combined forming a multistage amplifier. These stages are connected in cascade, i.e. output of the first stage is connected to the input of the second stage, whose output becomes the input of the third stage, and so on.

In this way the desirable characteristics (e.g. high voltage gain, high input resistance, low output resistance) of different single-transistor amplifiers (e.g. common-source, common-emitter, common-collector) can be combined to create an amplifier whose characteristics exceed those of a single-stage.[1]

A cascade amplifier is any two-port network constructed from a series of amplifiers, where each amplifier sends its output to the input of the next amplifier in a daisy chain.[2]

The complication in calculating the gain of cascaded stages is the non-ideal coupling between stages due to loading. Two cascaded common emitter stages are shown. Because the input resistance of the second stage forms a voltage divider with the output resistance of the first stage, the total gain is not the product of the individual (separated) stages.

## Overall gain

The overall gain of a multistage amplifier is the product of the gains of the individual stages (ignoring potential loading effects):

Gain (A) = A1* A2*A3 *A4 *... *An.

Alternately, if the gain of each amplifier stage is expressed in decibels (dB), the total gain is the sum of the gains of the individual stages:

Gain in dB (A) = A1 + A2 + A3 + A4 + ... An

## Inter-stage coupling

Depending on the manner in which the different amplifier stages are connected, one of the following amplifiers may result:

Transformer coupled amplifiers are often also tuned amplifiers. The inductance of the transformer windings serves as the inductor of a LC tuned circuit. If both sides of the transformer are tuned it is called a double-tuned amplifier. Staggered tuning is where each stage is tuned to a different frequency in order to improve bandwidth at the expense of gain.

## References

1. ^ Jaeger, Richard C. (2015). Microelectronic circuit design. Travis N. Blalock (Fifth ed.). New York, NY. ISBN 978-0-07-352960-8. OCLC 893721562.
2. ^ Innovatia: amplifier circuits