A differential amplifier is a circuit designed to amplify the difference between two input signals while rejecting any signals common to both (Common Mode Rejection). These amplifiers can be constructed using BJTs, FETs, or BiCMOS technology. While discrete implementations are possible, they are most commonly found within Integrated Circuits (ICs), where transistors can be perfectly matched on a single silicon substrate to ensure thermal stability and precision.
The differential amplifier serves as the critical input stage for Operational Amplifiers (Op-Amps). Depending on the input/output configuration, there are four primary types:
- Dual Input Balanced Output (DIBO)
- Dual Input Unbalanced Output (DIUO)
- Single Input Balanced Output (SIBO)
- Single Input Unbalanced Output (SIUO)
In this article, we focus on the Single Input Balanced Output (SIBO) BJT Differential Amplifier.
Single Input Balanced Output (SIBO) Configuration
In a SIBO configuration, a single input signal is applied to one transistor base while the other is grounded. The term "Balanced Output" refers to the fact that the output signal is measured between the collectors of the two transistors ($Q_1$ and $Q_2$).
Transistors $Q_1$ and $Q_2$ are matched pairs with identical $\beta$ and $V_{BE}$. Their collector resistors ($R_{C1}$ and $R_{C2}$) are also equal. Even though only one input ($V_1$) is active, the common emitter resistor ($R_E$) couples the signal to $Q_2$, allowing for a balanced differential output.
Circuit Analysis
By applying DC and AC analysis (using the h-parameter model), we can determine the operating point and gain characteristics:
DC Operating Point (Q-point):
$$I_{CQ} \approx \frac{V_{EE} - V_{BE}}{2R_E}$$$$V_{CEQ} = V_{CC} + V_{BE} - I_{CQ}R_C$$AC Parameters:
- Differential Gain ($A_{dm}$): $A_{dm} = \frac{h_{fe} R_C}{2(R_B + h_{ie})}$
- Input Resistance ($R_i$): $R_i = 2(R_B + h_{ie})$
- Output Resistance ($R_o$): $R_o = R_C$
Simulation and Waveform Analysis
To demonstrate, consider a circuit using 2N3904 transistors with $R_C = 100 \Omega$, $R_E = 100 \Omega$, and $R_B = 1k \Omega$. Applying a 50mV peak signal at 1kHz to $Q_1$ results in a differential output with a peak-to-peak voltage of approximately 2.28V (or 1.14V peak).
The calculated differential voltage gain for this setup is:
$$A_{dm} = \frac{V_{out(peak)}}{V_{in(peak)}} = \frac{1.14V}{50mV} \approx 23$$AC Coupled Configuration
For applications requiring the removal of DC offsets, coupling capacitors (e.g., 0.1µF) can be added to the collector outputs. This provides a pure AC differential signal centered at 0V.
Applications
BJT differential amplifiers are versatile components used in:
- The input stages of Operational Amplifiers.
- Communication circuits such as Voltage Controlled Oscillators (VCO).
- Modulation stages in signal processing.
