Widlar Current Mirror

The basic current mirror has a limitation when very small output currents are required. To generate low currents, the reference resistor ​R_1 must be very large. In integrated circuits, large resistor values occupy more chip area and are not economical to fabricate. To overcome this limitation, the Widlar Current Mirror is used.

• It is a modified version of the basic two-transistor current mirror in which an emitter degeneration resistor is added to the output transistor.
• This allows generation of very small output currents using moderate resistor values.

Need

In a basic current mirror:

• I_{\text{out}} \approx I_{\text{ref}}
• To obtain very small output current, I_{\text{ref}} must also be small
• Small I_{\text{ref}} requires a very large reference resistor
• Large resistors increase IC area and cost

Therefore, a better technique is needed to generate low currents efficiently.

Circuit Concept

In the Widlar current mirror:

• The reference transistor remains unchanged.
• An emitter resistor R_E is added to the output transistor.
• This introduces emitter degeneration.
• The base-emitter voltages are no longer equal: V_{BE1} \ne V_{BE2}

Because of this difference, the output current becomes significantly smaller than the reference current.

Mathematical Analysis

From the BJT current equation:

I_C = I_S e^{\frac{V_{BE}}{V_T}}

Taking the ratio of collector currents:

\frac{I_{C1}}{I_{C2}} = e^{\frac{V_{BE1}-V_{BE2}}{V_T}}

Taking natural logarithm:

V_{BE1} - V_{BE2} = V_T \ln\!\left(\frac{I_{C1}}{I_{C2}}\right)

Applying KVL in the emitter loop:

V_{BE1} - V_{BE2} = I_E R_E

Since I_E \approx I_C,

I_{C2} R_E = V_T \ln\!\left(\frac{I_{C1}}{I_{C2}}\right)

Let:

I_{C1} = I_{\text{ref}}, \quad I_{C2} = I_{\text{out}}

Then,

R_E = \frac{V_T}{I_{\text{out}}}\ln\!\left(\frac{I_{\text{ref}}}{I_{\text{out}}}\right)

This equation shows that very small output currents can be generated without using extremely large resistors.

Key Features

• Generates microampere-level currents
• Does not require very large reference resistor
• Uses exponential BJT characteristics
• Saves IC chip area
• Reduces noise due to emitter degeneration

Advantages

• Suitable for Low Current Generation : Efficient for microampere current sources.
• Reduced IC Area : Avoids very large resistor values.
• Improved Noise Performance : Emitter resistor reduces noise sensitivity.
• Better Thermal Stability : Emitter degeneration improves stability.
• Simple Modification : Only one additional resistor required.

Disadvantages

• Output Current Less Accurate Than Wilson Mirror : The current matching accuracy is lower compared to Wilson mirror due to limited output resistance.
• Reduced Output Voltage Compliance : The voltage drop across the emitter resistor reduces the minimum usable output voltage range.
• Slightly Increased Circuit Complexity : An additional emitter resistor makes the circuit slightly more complex than a basic mirror.
• Power Dissipation in Emitter Resistor : Some power is lost as heat in the emitter resistor during operation.

Applications

1. Biasing in Analog Integrated Circuits : Used to provide stable low-value bias currents inside analog ICs.

2. Low Current Reference Generation : Generates precise microampere-level reference currents.

3. Differential Amplifiers : Supplies controlled tail current in differential amplifier stages.

4. Operational Amplifier Bias Networks : Forms part of internal current biasing circuitry in op-amps.

5. Current Steering Circuits : Used in circuits where accurate low currents must be directed between branches.