Q10Analog Electronics

A multistage (cascaded) amplifier consists of two or more amplifier stages connected in series, where the output of one stage drives the input of the next. The stages may be coupled using RC coupling, direct coupling, or transformer coupling. The overall voltage gain is the product of individual stage gains:

In decibels: $A_v(dB)=A_{v1}(dB)+A_{v2}(dB)+\cdots +A_{vn}(dB)$

• A single amplifier stage cannot provide sufficient gain for most practical applications (e.g., amplifying microphone signals to speaker levels requires gains of 10,000 or more).
• Cascading allows achieving high gain while each stage operates at reasonable bias levels.
• Different stages can be optimized for different purposes: the first stage for low noise, subsequent stages for high gain.
• Cascading allows impedance matching between source and load through intermediate stages.

Each amplifier stage has an upper cutoff frequency $f_H$ and lower cutoff frequency $f_L$. When $n$ identical stages are cascaded, the overall bandwidth narrows. The new upper and lower cutoff frequencies are:

For 2 identical stages: $f_H^{\prime }\approx 0.644f_H$ (bandwidth reduced to 64.4% of single stage). For 3 stages: $f_H^{\prime }\approx 0.510f_H$. This gain-bandwidth tradeoff is a fundamental limitation: as gain increases with more stages, the bandwidth shrinks.

• RC Coupling: Most common. Capacitor blocks DC between stages; good for audio frequencies. Bandwidth limited at low frequencies.
• Direct Coupling: No coupling element; DC levels directly connected. Useful for amplifying very low frequency (DC) signals. Used in Op-Amps.
• Transformer Coupling: Provides impedance matching; good for RF. Bulky and expensive.