Electronics · Ch 5 — Operational Amplifiers

Applications of op-amp with negative feedback

5.4

Applications of op-amp with negative feedback

The applications of an op-amp are broadly classified as linear and non-linear:

Linear applications — the output is directly proportional to the input. Examples: the inverting amplifier and the non-inverting amplifier.
Non-linear applications — the output is not directly proportional to the input. Examples: the integrator, the differentiator and the logarithmic amplifier.

Why feedback is needed. An op-amp has a very high open loop gain, so on its own it can amplify only very small signals without distortion. For any larger signal the output tries to exceed the supply voltages $+V_{CC}$ and $-V_{EE}$ , and clipping occurs. To make the device usable, negative feedback is applied — a portion of the output is fed back to the input, either directly or through a resistor network. With feedback the op-amp becomes a very versatile device usable over a wide range of AC and DC applications, and its overall gain is set by the external resistors rather than by the huge, variable open loop gain.

Virtual ground (virtual short) concept. Consider an ideal op-amp with negative feedback (Figures 5.4.1 and 5.4.2). Let $V_A$ be the voltage at the inverting terminal, $V_B$ the voltage at the non-inverting terminal, $i_b$ the current into the op-amp, and $R_i$ , $R_f$ the input and feedback resistors. For an ideal op-amp the open loop gain $A = \infty$ and the input impedance $Z_i = \infty$ . Since

A = \frac{V_O}{V_B - V_A} = \infty \;\Rightarrow\; V_B - V_A = 0 \;\Rightarrow\; V_A = V_B

So the two input terminals always sit at the same voltage (a virtual short). If $V_B$ is grounded then $V_A = 0$ : the inverting terminal is at zero volts even though it is not physically connected to ground — this is the virtual ground. And because $Z_i = \infty$ , no current enters the op-amp, i.e. $i_b = 0$ . Note the virtual ground holds for voltage only, not for current flow. This single idea makes every feedback derivation below straightforward.

Inverting amplifier. An inverting amplifier gives an output that is 180° out of phase with the input. The input $V_i$ is applied to the inverting terminal through $R_i$ , the non-inverting terminal is grounded, and $R_f$ is the feedback resistor from output to the inverting node A (Figure 5.4.3). With the virtual ground $V_A = 0$ and $i_b = 0$ , applying KCL at node A gives $i_i = i_f$ :

\frac{V_i - V_A}{R_i} = \frac{V_A - V_O}{R_f}

Putting $V_A = 0$ : $\dfrac{V_i}{R_i} = \dfrac{-V_O}{R_f}$ , so

V_O = -\frac{R_f}{R_i}\,V_i \qquad A_V = \frac{V_O}{V_i} = -\frac{R_f}{R_i}

The minus sign shows the 180° phase inversion.

Inverter (sign changer). The inverter is a special case of the inverting amplifier that produces an output equal in magnitude but opposite in phase to the input. It is obtained by making $R_f = R_i$ (Figure 5.4.4, both resistors labelled R), which gives

V_O = -V_i

The output is simply the inversion of the input, and the circuit is called an op-amp inverter.

Non-inverting amplifier. A non-inverting amplifier gives an output in phase with the input. The input $V_i$ is applied to the non-inverting terminal, the inverting terminal is grounded through $R_i$ , and $R_f$ is the feedback resistor (Figure 5.4.5). Now $V_B = V_A = V_i$ and $i_b = 0$ . Applying KCL at node A ( $i_i = i_f$ ):

\frac{0 - V_A}{R_i} = \frac{V_A - V_O}{R_f}

Putting $V_A = V_i$ and solving:

V_O = V_i\left(1 + \frac{R_f}{R_i}\right) \qquad A_V = \frac{V_O}{V_i} = 1 + \frac{R_f}{R_i}

The gain is always greater than one and the output is in phase with the input. …

Definition 1Virtual ground (virtual short)

In an ideal op-amp with negative feedback, the infinite open loop gain forces the two input terminals to the same voltage, $V_A = V_B$ . When the non-inverting terminal is grounded, the inverting terminal sits at 0 V without being physically grounded — a virtual ground. Infinite input impedance also makes the current into the op-a …

Figure 2Ideal op-amp with negative feedback illustrating the virtual ground concept at the inverting input node