The Wilson current source is a three-transistor active load circuit that delivers a highly stable, precise output current by using negative feedback to cancel out the base-current errors and Early effect variations found in basic current mirrors. In a real circuit or installation, swapping a basic two-transistor mirror for a Wilson topology changes the output impedance from a mediocre, voltage-dependent value to a massive, nearly ideal resistance, effectively making the current source 'stiff' against voltage fluctuations at the output node. This stiffness is critical when biasing high-gain differential pairs where even microamp-level current drifts ruin the common-mode rejection ratio (CMRR).
The Core Topology and Why Basic Mirrors Fail
To understand why the Wilson topology exists, you first have to look at the flaws of the standard two-transistor current mirror. In a basic NPN mirror, the reference transistor (Q1) is diode-connected, and its base-emitter voltage drives the output transistor (Q2). This setup suffers from two major silicon-level realities:
- Base Current Error: The reference current ($I_{REF}$) must supply the base currents for both Q1 and Q2. Therefore, the output collector current ($I_{OUT}$) is always slightly less than $I_{REF}$ by a factor of $2/\beta$. For a typical small-signal BJT with a $\beta$ of 100, you immediately lose 2% of your current accuracy.
- The Early Effect: As the voltage across the output transistor ($V_{CE}$) increases, the effective base width narrows, causing $I_{OUT}$ to slope upward. The output impedance is limited to the transistor's intrinsic output resistance ($r_o$), which might only be 50k$\Omega$ to 100k$\Omega$ at typical bias currents.
The Wilson current source solves this by introducing a third transistor (Q3). Q1 and Q2 still form the core mirror, but Q3 is inserted to feed the output current back into the base drive network. Think of a basic current mirror as a single-lane road where a few cars (base current) leak off at every intersection; the Wilson topology adds a feedback on-ramp that forces those leaked cars back into the main lane, ensuring the exact same traffic volume reaches the destination. By forcing the collector voltage of Q1 to remain relatively constant, the Wilson circuit also heavily mitigates the Early effect mismatch between Q1 and Q2.
Topology Comparison: Basic, Wilson, and Cascode Mirrors
When designing the biasing network for an amplifier, you have several active load topologies to choose from. The table below maps the exact theoretical performance of these circuits assuming a matched NPN pair with a $\beta$ of 150 and an intrinsic $r_o$ of 50k$\Omega$.
| Topology | Transistor Count | Output Impedance ($R_{out}$) | Current Transfer Error | Min. Output Headroom ($V_{min}$) |
|---|---|---|---|---|
| Basic Mirror | 2 | $r_o$ (50k$\Omega$) | $2/\beta$ (1.33%) | $V_{CE(sat)}$ (~0.2V) |
| Wilson Mirror | 3 | $\beta r_o / 2$ (3.75M$\Omega$) | $2/\beta^2$ (0.0088%) | $V_{CE(sat)} + V_{BE}$ (~0.85V) |
| Improved Wilson | 4 | $\beta r_o$ (7.5M$\Omega$) | $2/\beta^2$ (0.0088%) | $2V_{BE}$ (~1.3V) |
| Cascode Mirror | 4 | $\beta r_o$ (7.5M$\Omega$) | $2/\beta$ (1.33%) | $V_{CE(sat)} + V_{BE}$ (~0.85V) |
As the data shows, the Wilson mirror provides a massive 75x increase in output impedance over the basic mirror while simultaneously reducing the static current error to negligible levels. However, this comes at the cost of voltage headroom, a critical trade-off in low-voltage battery-powered designs.
Worked Numeric Example: Calculating Output 'Stiffness'
Let's run the exact math for a discrete Wilson current source built using a matched dual NPN transistor like the BCM847 (or two tightly matched 2N3904s). We will bias the circuit with a reference current ($I_{REF}$) of 2.0 mA.
Assumed Silicon Parameters:
- DC Current Gain ($\beta$): 150
- Early Voltage ($V_A$): 100V
- Thermal Voltage ($V_T$): 26mV at room temperature
Step 1: Calculate Intrinsic Output Resistance ($r_o$)
The Early effect defines the baseline slope of the collector current.
$r_o = V_A / I_C = 100V / 2.0mA = 50,000\Omega$ (50k$\Omega$).
Step 2: Calculate Basic Mirror Performance
If we used a standard 2-transistor mirror, the output impedance would simply be $r_o = 50k\Omega$.
If the output voltage swings by 5V, the current would drift by $\Delta I = \Delta V / r_o = 5V / 50k\Omega = 100\mu A$. For a 2mA bias, a 100$\mu A$ drift is a 5% variation—unacceptable for precision analog stages.
Step 3: Calculate Wilson Mirror Performance
The Wilson topology multiplies the output impedance by approximately $\beta / 2$.
$R_{out(Wilson)} \approx (150 \times 50,000) / 2 = 3,750,000\Omega$ (3.75M$\Omega$).
Now, if the output voltage swings by that same 5V, the current drift is $\Delta I = 5V / 3.75M\Omega = 1.33\mu A$. This is a mere 0.06% variation, rendering the current source virtually immune to output voltage swings.
Step 4: Verify the Static Current Error
The Wilson feedback loop forces the output current to match the reference current with an error factor of roughly $2/\beta^2$.
Error = $2 / (150)^2 = 2 / 22,500 = 0.000088$, or 0.0088%. At a 2mA reference, the static mismatch is less than 176 nanoamps.
Where You Meet This in Practice and Common Confusions
You rarely build a Wilson current source from discrete components on a breadboard unless you are designing a high-end Class AB audio amplifier from scratch. In discrete audio designs (like those popularized by Bob Cordell or Douglas Self), the input Long-Tailed Pair (LTP) requires an incredibly stiff tail current source to achieve high CMRR and reject power supply ripple. A basic mirror will let power supply noise modulate the tail current, but a Wilson mirror locks it down.
However, you interact with Wilson current sources every time you use an integrated operational amplifier. Inside the silicon of precision op-amps like the OP07 or modern Analog Devices instrumentation amplifiers, Wilson and Improved Wilson mirrors are used as the active loads for the differential input stages. They provide the massive voltage gain required in the first stage by presenting a multi-megaohm impedance to the collector nodes of the input pair.
What do people commonly confuse the Wilson current source with?
The Widlar Current Source: The Widlar mirror uses an emitter degeneration resistor on the output transistor to generate extremely small microamp-level currents from a milliamp-level reference. The Wilson mirror uses no emitter resistors; it relies purely on active transistor feedback for high impedance and accuracy.
The Cascode Current Mirror: Both the Wilson and the Cascode mirror achieve high output impedance ($\beta r_o$). However, the Cascode stacks a common-base transistor on top of a common-emitter transistor. The Cascode requires an extra transistor (4 total for a fully matched version) and requires a separate bias voltage generator for the cascode gate/base, whereas the Wilson is self-biasing with just 3 transistors.
The Improved Wilson Mirror: The standard 3-transistor Wilson mirror has a slight flaw: the collector-emitter voltages of Q1 and Q2 are not perfectly equal, which introduces a tiny Early effect mismatch. The 'Improved' Wilson adds a fourth diode-connected transistor to equalize these voltages, pushing the output impedance up to $\beta r_o$ and eliminating the theoretical zero-current latch-up state.
When selecting a topology for your next analog build, look at your voltage rails and your required precision. If you have the headroom and need nanoamp-level stability without resorting to expensive laser-trimmed resistors, the Wilson current source remains one of the most elegant and powerful circuit topologies in analog electronics.
