Operational Amplifier

Having seen the differential amplifier at its input, we now look at the op-amp as a complete device through its AC equivalent circuit and its characteristics.

AC equivalent circuit. Figure 5.3.1 shows the op-amp modelled in both a practical and an ideal form. In the practical model a differential input voltage $V_d$ appears across the two input terminals, an input resistance $R_i$ is drawn between them, and a dependent voltage source $A_d V_d$ drives the output through an output resistance $R_o$; the device is powered by $+V_{CC}$ and $-V_{EE}$. In the ideal model there is no input-resistance branch ($R_i = \infty$) and no output resistance ($R_o = 0$), so the dependent source $A_d V_d$ connects straight to the output.

Ideal vs practical characteristics. A practical op-amp has very high input impedance $R_i$, very high voltage gain $A_d$ and low output impedance $R_o$; an ideal op-amp has infinite input impedance, infinite voltage gain and zero output impedance. The main characteristics are:

• Open Loop Gain — the gain of the amplifier without feedback. It is infinite for an ideal op-amp and of the order of $10^5$ for a practical one.
• Input Impedance — the impedance seen looking into the two input terminals. Ideally infinite, so the op-amp can be driven by any source without loading the previous stage; practically a few $M\Omega$.
• Output Impedance — the impedance seen looking back into the output terminal. Ideally zero, so the op-amp can drive any number of devices without getting loaded; practically a few tens of $\Omega$.
• Bandwidth — ideally infinite, meaning the op-amp amplifies signals from zero to infinite hertz without attenuation; practically a few MHz.
• CMRR — the ability to reject common-mode signals such as noise while amplifying differential signals. Ideally infinite; a practical value is around 90 dB.
• Slew Rate — the maximum rate of change of the output voltage when a large signal is applied to the closed-loop amplifier. It shows how well the op-amp handles rapidly varying signals (its response to changes in input). For an ideal op-amp the response time is zero, so the slew rate is infinite. Its unit is V/μs and it is given by $\text{Slew Rate} = \dfrac{\Delta V_O}{\Delta t}$.

Input offset voltage. Ideally, when the two inputs are at the same voltage the output should be zero, since $V_O = A_d(V_1 - V_2)$. In practice it is not, so a small voltage — the input offset voltage $V_{io}$ — must be applied between the two input terminals to force the output to zero. This is also called the balancing technique and is shown in Figure 5.3.2. …