The non- ideal characteristics of op-amp which are DC and AC are:

DC error components are:

#### Input Bias Current:

The input bias current of an operational amplifier is the average of the two currents flowing at the inverting and non-inverting terminal respectively. The mathematical equation is given by:

IB = (IB++IB)/2 ##### For a Basic inverting op-amp :

If V1 = 0, then output voltage is offset given by,

V0 = IB – Rf1

For 741 op-amp, Rf  = 1mΩ and input bias current is 500mA or less.

Therefore, output voltage is driven to 500mV.

In applications where signal levels are measure in milli-volts it is totally unacceptable. Hence, a compensated resistor is added between non-inverting input terminal and ground. Current IB+ going through the compensator resistor has a voltage V1 across it

From KVL,

-V1 + 0 + V2 – V0 = 0

By selecting proper value of Rcomp V2 and be cancelled with V1 to make V0

Therefore, V1 =IB+ Rcomp ­ (or)

IB+ = V1/ Rcomp _(A)

At mode ‘a’ voltage (-V1) exists because voltage at non-inverting terminal is (-V1)

Therefore, when Vi = 0

I1 = V1/R1 and I2 = Vc / Rf

For compensation V0 = 0 for, Vi =0

Therefore, From V2 = V1 = 0 => V1 = V2

I2 = V1 / Rf

KCL at node ‘a’

IB = I2 + I1

IB = V1/R1 +  V1 / Rf
= V1 [ 1/ R1 + 1 / Rf ]

= V1 [ (R1 + Rf )/ R1Rf ] __(B)

By equating   (A) and (B)

V1/ Rcomp = V1 [ (R1 + Rf )/ R1Rf ]

V1/ Rcomp = (R1 + Rf )/ R1Rf