A current mirror is a fundamental building block in analog integrated circuit design. It is an active circuit designed to copy or "mirror" a current flowing through one device by controlling the current in another active device of the same type. By keeping the output current constant regardless of loading, it effectively functions as a current regulator or a constant current source.
How it Works
A basic current mirror typically consists of two matched transistors—either Bipolar Junction Transistors (BJTs) or Field-Effect Transistors (FETs). One transistor is "diode-connected" at the input, translating the input reference current into a specific gate-to-source or base-to-emitter voltage. This voltage is then applied to the second transistor, which reproduces the same current at its collector or drain.
Applications of Current Mirrors
- DC Biasing: Used in Integrated Circuits (ICs) to establish a stable Q-point for amplifiers, ensuring they remain in the active region despite temperature fluctuations.
- Active Loads: Replaces bulky resistors in operational amplifiers to achieve significantly higher voltage gain.
- Current Steering: Distributes a single reference current to multiple branches of a complex circuit.
The following shows the circuit diagram of a BJT-based current mirror.
Mathematical Derivation
In the circuit above, transistor $T_1$ is diode-connected (collector shorted to base). This ensures $T_1$ is always in the active region or cutoff, never saturation. To function accurately, $T_1$ and $T_2$ must be matched—ideally fabricated on the same silicon substrate to ensure identical physical properties.
Assuming matched transistors, we have:
$$\beta_1 = \beta_2 = \beta$$$$V_{BE1} = V_{BE2} = V_{BE}$$$$I_{B1} = I_{B2} = I_B$$Applying Kirchhoff’s Current Law (KCL) at the collector node of $T_1$:
$$I_R = I_{C1} + I_{B1} + I_{B2}$$$$I_R = I_{C1} + 2I_B$$Since $I_B = \frac{I_{C1}}{\beta}$ and $I_{C1} = I_{C2} = I_O$ (due to matching):
$$I_R = I_O + \frac{2I_O}{\beta} = I_O \left(1 + \frac{2}{\beta}\right)$$Solving for the output current $I_O$:
$$I_O = \frac{I_R}{1 + \frac{2}{\beta}}$$If the current gain $\beta$ is very large ($\beta \gg 1$), the term $\frac{2}{\beta}$ becomes negligible, leading to:
$$I_O \approx I_R$$The reference current $I_R$ is set by the supply voltage and the resistor $R$:
$$I_R = \frac{V_{CC} - V_{BE}}{R}$$Conclusion
Current mirrors are indispensable for precision analog design. While the simple BJT mirror is effective, advanced versions like the Wilson Current Mirror or the Widlar Current Mirror are used in high-performance voltage regulators and operational amplifiers to further reduce the impact of finite $\beta$ and the Early Effect. By mastering this building block, you can design circuits with highly stable DC biasing and superior linear performance.
