Why learn negative feedback amplifier design

I came across an amplifier circuit diagram of multistage amplifier built with BJT transistors. The circuit illustrated negative feedback amplifier design. I always wanted to learn transistors based circuit with negative and positive feedback. Negative feedback design with op-amp also called inverting amplifier is easy to understand but the negative feedback used in amplifier design with transistor is bit different. Below is the circuit diagram of the negative feedback amplifier designed with BJT transistors.

negative feedback amplifier design with transistors

A two-stage transistor amplifier with negative feedback uses two cascaded common-emitter amplifier stages, where the output of the second stage is fed back to the emitter of the first stage through a resistor-capacitor (RC) network. This design helps stabilize the amplifier’s gain, improves linearity, reduces distortion, and expands bandwidth. The first transistor is biased using a voltage divider and includes emitter resistors for thermal stability. Negative feedback reduces overall gain but makes it more predictable and less sensitive to temperature and transistor variations. Capacitive coupling between stages and in the feedback path ensures AC signal flow while blocking DC, preserving bias points. Learning to design such circuits deepens understanding of core analog electronics concepts like biasing, feedback, small-signal analysis, gain control, and amplifier stability without relying on op-amps or ICs.

✅ 1. Overview of Your Amplifier Circuit

Stage 1:

Transistor: 2N2222
Biasing: Voltage divider (R1 = 10kΩ, R2 = 2.2kΩ)
Emitter resistor: Re = 180Ω + R3 = 820Ω → total = 1000Ω
Collector resistor: R4 = 3.6kΩ
Feedback resistor: Rf = 180Ω from Stage 2 output to emitter via C6 = 0.1µF

Stage 2:

Also a 2N2222 with same biasing setup (implied)
Its output (collector) feeds back through capacitor C6 and resistor Rf

Input Signal:

1kHz sine wave, 200 mV amplitude

Mathematics of negative feedback amplifier

🧮 Feedback Fraction (β)

Given:

$R_e = 180\ \Omega$
$R_f = 10\,000\ \Omega$

Then the feedback fraction β becomes:

\beta = \frac{R_e}{R_e + R_f} = \frac{180}{180 + 10\,000} \approx 0.0176 \text{ (or 1.76%)}

This is now much smaller, meaning less feedback — so:

The gain is higher, but
The feedback benefits (like distortion reduction, bandwidth extension) are weaker

📐 Closed-Loop Gain (Af)

If the open-loop gain A is large (say ~1000, typical for a two-stage BJT amplifier), the closed-loop gain becomes:

A_f = \frac{A}{1 + A\beta} \approx \frac{1}{\beta} = \frac{1}{0.0176} \approx 56.8

So you now get a closed-loop voltage gain of approximately 57×, or 35 dB — which is a significant amplification.

📉 Feedback Cutoff Frequency

Now, your high-pass cutoff frequency due to C6 and the feedback resistors is:

f_c = \frac{1}{2\pi(R_f + R_e)C_6} = \frac{1}{2\pi \cdot (10\,000 + 180) \cdot 10 \times 10^{-6}} \approx 1.56\ \text{Hz}

➡️ This is excellent — it means your feedback loop is effective even at very low frequencies, including your 1 kHz signal.

The following shows the input and output signal waveform.