Chapter Summary

Operational Amplifiers — chapter summary

• An operational amplifier (op-amp) is a high-gain, direct-coupled differential amplifier. An ideal op-amp has infinite open-loop gain, infinite input impedance and zero output impedance; the virtual-ground concept ($V_A = V_B = 0$) and zero input bias current are the two tools used to analyse almost every op-amp circuit.
• In its linear (negative-feedback) applications the op-amp works as an inverting amplifier, non-inverting amplifier, voltage follower (buffer), summing amplifier and difference amplifier. The summing amplifier gives $V_O = -R_f\left(\dfrac{V_1}{R_1} + \dfrac{V_2}{R_2} + \dfrac{V_3}{R_3}\right)$, reducing to $V_O = -(V_1 + V_2 + V_3)$ for equal resistors; the subtractor gives $V_O = V_2 - V_1$ for equal resistors.
• Among the non-linear applications, the differentiator gives $V_O = -R_f C\,\dfrac{d(V_i)}{dt}$ (needs $RC < 10T$) and the integrator gives $V_O = -\dfrac{1}{R_i C}\int V_i\,dt$ (needs $RC > 10T$). A logarithmic amplifier (diode in feedback) gives an output proportional to $\log_e(V_i)$, and an anti-logarithmic amplifier (diode at the input) gives an output proportional to the antilog of the input; a log-adder-antilog chain multiplies two signals, $V_O \propto V_1 \times V_2$.
• Active filters combine an RC network with an op-amp non-inverting amplifier. A first-order low-pass or high-pass filter has cut-off frequency $f_c = \dfrac{1}{2\pi R_1 C_1}$ and gain $A_V = 1 + \dfrac{R_f}{R_i}$; second-order versions roll off faster and approach the ideal response.
• A DAC converts a digital code into a proportional analog voltage, using either an R-2R ladder network or a binary weighted resistance network feeding a summing amplifier. An ADC does the reverse; the counting ADC uses a comparator, binary counter, DAC and AND gate, comparing a rising DAC staircase against the analog input. …