Question

Derive relation for output offset voltage due to input biasing current

Answer 1

Build any op amp circuit, apply 0V to its input, and what do you expect at the output? Although you'd be tempted to say 0 V, there's actually an error voltage present at its output. What causes this error? You can trace the error back to a number of unbalances in the op amp's internal transistors and resistors. To account for this in a circuit design, the net error is modeled as an offset voltage, Voff, in series with op amp's input terminals. How will it affect your circuit? That depends on the op amp itself and your circuit design.

INPUT OFFSET VOLTAGE

The input offset voltage can range from microvolts to millivolts and can be either polarity. Generally, bipolar op amps have lower offset voltages than JFET or CMOS types.

But wait, there's more trouble. The input offset voltage will change ∆V (voltage drift) with a change in temperature ∆T. This error is a linear function of temperature and is defined by

Voff_TC = ∆Voff / ∆T (V/deg C)

For an with a voltage of 25 uV / deg C, what is the drift over, say ∆T = 10 deg C?

Voff = Voff_TC · ∆T

= (25 uV / deg C) · 10 deg C

= 0.25 mV

This could add some serious error into your temperature senor circuit! But, knowing your overall error budget, you can select an op amp with a low enough offset drift to meet the target circuit performance.

AMPLIFIER WITH OFFSET VOLTAGE

The offset voltage is modeled in series with one of the op amp input terminals. Which one? Although the net effect is the same at either input, it's much easier to analyze Voff in series with the positive (V+) input. Why? The resulting circuit with Voff at V+ looks just like the non-inverting amplifier configuration. The analysis for this circuit is a simple one.

Ignoring Voff for a moment, is the circuit (shown above) an inverting or non-inverting amplifier? The answer is yes, both! With the input signal source set to 0 V ( shorted ), the inverting and non-inverting amplifiers look the same. The analysis for offset voltage is independent of the amplifier configuration. You can predict the error at the output Vo by the equation for the non-inverting amplifier

Vo_error = Voff ( R2 / R1 + 1 )

What danger is this equation warning you about? If you have a large signal gain in your circuit, the amplifier will increase the error Voff along with the signal.

CIRCUIT INSIGHT Run a simulation of OP_VOFF.CIR. Voltage source VOFF models the offset voltage, initially set to +1 mV. With R1 = 10k and R2 = 100 k, what is the error at the output V(4)? The output error gets bumped to a whopping 11 mV as predicted by the equation above. Choose a different gain and/or offset voltage. Run a simulation. Is the output error what you expected?

OFFSET ADJUSTMENT

Need to adjust the the effect of the input offset voltage to zero? Add a potentiometer and a resistor.(See Op Amp Input Offset Adjustment)

INPUT BIAS CURRENT

Input offset voltage is not the only error of the op amp's input. The input stage is made of transistors, requiring a finite amount of bias current for operation. The circuit above assumes the bias is negligible. However, real op amps have bias currents to be reckoned with. The good news is there are clever techniques you can use to minimize and cancel out these errors too.

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