# Non-zero Input Bias Current - Operational Amplifiers Types Tutorials Series

http://www.ingenuitydias.com/2015/02/non-zero-input-bias-current-operational.html

Effect of Non-zero Input Bias Currents

•In practice op-amps do not actually have zero input currents, but rather have very small input currents labeled I+ and I- in the figure at the left

–Modeled as internal current sources inside op-amp

–I+ and I- are both the same polarity

•e.g. if the input transistors are NPN bipolar devices, positive I+ and I- are required to provide base current

–In order to allow for slightly different values of I+ and I-, we define the term IBIAS as the average of I+ and I-

•In practice op-amps do not actually have zero input currents, but rather have very small input currents labeled I+ and I- in the figure at the left

–Modeled as internal current sources inside op-amp

–I+ and I- are both the same polarity

•e.g. if the input transistors are NPN bipolar devices, positive I+ and I- are required to provide base current

–In order to allow for slightly different values of I+ and I-, we define the term IBIAS as the average of I+ and I-

IBIAS = ½ (I+ + I-)

•Example: Given the op-amp shown in the bottom figure, derive an expression for vout that includes the effect of input bias currents

–Assume I+ = I- = 100 nA

–Using the virtual short condition and KCL, we can write vIN/R1 = I- + (0-vOUT)/R2 or

vOUT = - (R2/R1)vIN + I-R2

–Plugging in values gives vOUT = - 20 vIN + 2 mV

Correcting for Non-zero Input Bias Current

•The effect of non-zero input bias current can be zero’ed out by inserting a resistor Rx in series with the V+ input terminal (as shown)

–This same correction works for both inverting and non-inverting op-amps

–We choose Rx such that the dc component on the output caused by I+ exactly cancels the dc component on vOUT caused by I-

–One can use either KCL (Kirchhoff’s Current Law) or superposition to show that choosing Rx = R1 || R2 completely cancels out the dc effect of non-zero input bias current

•KCL Method (inverting op-amp at left)

–vIN is applied to R1 and Rx is grounded

–v- = v+ = 0 – I+Rx due to virtual short

–Apply KCL to v+ input:

(vIN – v-)/R1 = I- + (v- - vOUT)/R2

–Solve for vOUT and substitute –I+Rx for v-

vOUT = - (R2/R1) vIN + I-R2 – I+Rx(R1 + R2)/R1

–Setting the dc bias terms equal yields

Rx = R1 || R2 = R1 R2/(R1 + R2)

•Example: Given the op-amp shown in the bottom figure, derive an expression for vout that includes the effect of input bias currents

–Using the virtual short condition and KCL, we can write vIN/R1 = I- + (0-vOUT)/R2 or

vOUT = - (R2/R1)vIN + I-R2

–Plugging in values gives vOUT = - 20 vIN + 2 mV

Correcting for Non-zero Input Bias Current

•The effect of non-zero input bias current can be zero’ed out by inserting a resistor Rx in series with the V+ input terminal (as shown)

–This same correction works for both inverting and non-inverting op-amps

–We choose Rx such that the dc component on the output caused by I+ exactly cancels the dc component on vOUT caused by I-

–One can use either KCL (Kirchhoff’s Current Law) or superposition to show that choosing Rx = R1 || R2 completely cancels out the dc effect of non-zero input bias current

•KCL Method (inverting op-amp at left)

–vIN is applied to R1 and Rx is grounded

–v- = v+ = 0 – I+Rx due to virtual short

–Apply KCL to v+ input:

(vIN – v-)/R1 = I- + (v- - vOUT)/R2

–Solve for vOUT and substitute –I+Rx for v-

vOUT = - (R2/R1) vIN + I-R2 – I+Rx(R1 + R2)/R1

–Setting the dc bias terms equal yields

Rx = R1 || R2 = R1 R2/(R1 + R2)