The first example is the differential amplifier, from which many of the other applications can be derived, including the
inverting,
non-inverting, and
summing amplifier, the
voltage follower,
integrator,
differentiator, and
gyrator.
Differential amplifier (difference amplifier) Amplifies the difference in voltage between its inputs. :The name "differential amplifier" must not be confused with the "
differentiator", which is also shown on this page. :The "
instrumentation amplifier", which is also shown on this page, is a modification of the differential amplifier that also provides high
input impedance. The circuit shown computes the
difference of two voltages, multiplied by some gain factor. The output voltage :V_\text{out} = \frac{\left( R_\text{f} + R_1 \right) R_\text{g}}{\left( R_\text{g} + R_2 \right) R_1} V_2 - \frac{R_\text{f}}{R_1} V_1 = \left( \frac{R_1 + R_\text{f}}{R_1} \right) \cdot \left( \frac{R_\text{g}}{R_\text{g} + R_2} \right) V_2 - \frac{R_\text{f}}{R_1} V_1. Or, expressed as a function of the common-mode input
Vcom and difference input
Vdif: :V_\text{com} = (V_1 + V_2) / 2; V_\text{dif} = V_2 - V_1, the output voltage is :V_\text{out} \frac{R_1}{R_\text{f}} = V_\text{com} \frac{R_1 / R_\text{f} - R_2 / R_\text{g}}{1 + R_2 / R_\text{g}} + V_\text{dif} \frac{1 + (R_2 / R_\text{g} + R_1 / R_\text{f}) / 2}{1 + R_2 / R_\text{g}}. In order for this circuit to produce a signal proportional to the voltage difference of the input terminals, the coefficient of the
Vcom term (the common-mode gain) must be zero, or :R_1 / R_\text{f} = R_2 / R_\text{g}. With this constraint in place, the
common-mode rejection ratio of this circuit is infinitely large, and the output :V_\text{out} = \frac{R_\text{f}}{R_1} V_\text{dif} = \frac{R_\text{f}}{R_1} \left(V_2 - V_1\right), where the simple expression
Rf /
R1 represents the closed-loop gain of the differential amplifier. The special case when the closed-loop gain is unity is a differential follower, with :V_\text{out} = V_2 - V_1.
Inverting amplifier An inverting amplifier is a special case of the
differential amplifier in which that circuit's non-inverting input
V2 is grounded, and inverting input
V1 is identified with
Vin above. The closed-loop gain is
Rf /
Rin, hence :V_{\text{out}} = -\frac{R_{\text{f}}}{R_{\text{in}}} V_{\text{in}}\!\,. The simplified circuit above is like the differential amplifier in the limit of
R2 and
Rg very small. In this case, though, the circuit will be susceptible to input bias current drift because of the mismatch between
Rf and
Rin. To intuitively see the gain equation above, calculate the current in
Rin: : i_{\text{in}} = \frac{ V_{\text{in}} }{ R_{\text{in}} } then recall that this same current must be passing through
Rf, therefore (because
V− =
V+ = 0): : V_{\text{out}} = -i_{\text{in}} R_{\text{f}} = - V_{\text{in}} \frac{ R_{\text{f}} }{ R_{\text{in}} } A mechanical analogy is a seesaw, with the
V− node (between
Rin and
Rf) as the fulcrum, at ground potential.
Vin is at a length
Rin from the fulcrum;
Vout is at a length
Rf. When
Vin descends "below ground", the output
Vout rises proportionately to balance the seesaw, and
vice versa. As the negative input of the op-amp acts as a virtual ground, the input impedance of this circuit is equal to
Rin.
Non-inverting amplifier A non-inverting amplifier is a special case of the
differential amplifier in which that circuit's inverting input
V1 is grounded, and non-inverting input
V2 is identified with
Vin above, with
R1 ≫
R2. Referring to the circuit immediately above, :V_{\text{out}} = \left(1 + \frac{ R_{\text{2}} }{ R_{\text{1}} } \right) V_{\text{in}}\!\,. To intuitively see this gain equation, use the virtual ground technique to calculate the current in resistor
R1: : i_1 = \frac{ V_{\text{in}} }{ R_1 }\,, then recall that this same current must be passing through
R2, therefore: : V_{\text{out}} = V_{\text{in}} + i_1 R_2 = V_{\text{in}} \left( 1 + \frac{ R_2 }{ R_1 } \right) Unlike the inverting amplifier, a non-inverting amplifier cannot have a gain of less than 1. A mechanical analogy is a
class-2 lever, with one terminal of
R1 as the fulcrum, at ground potential.
Vin is at a length
R1 from the fulcrum;
Vout is at a length
R2 further along. When
Vin ascends "above ground", the output
Vout rises proportionately with the lever. The input impedance of the simplified non-inverting amplifier is high: : Z_{\text{in}} = (1+A_\text{OL}B)Z_{\text{dif}} where
Zdif is the op-amp's input impedance to differential signals, and
AOL is the open-loop voltage gain of the op-amp (which varies with frequency), and
B is the
feedback factor (the fraction of the output signal that returns to the input). In the case of the ideal op-amp, with
AOL infinite and
Zdif infinite, the input impedance is also infinite. In this case, though, the circuit will be susceptible to input bias current drift because of the mismatch between the impedances driving the
V+ and
V− op-amp inputs. The feedback loop similarly decreases the output impedance: : Z_{\text{out}} = \frac{Z_{\text{OL}}}{1+A_\text{OL}B} where
Zout is the output impedance with feedback, and
ZOL is the open-loop output impedance.
Voltage follower (unity buffer amplifier) Used as a
buffer amplifier to eliminate loading effects (e.g., connecting a device with a high
source impedance to a device with a low
input impedance). : V_{\text{out}} = V_{\text{in}} \! :Z_{\text{in}} = \infty (realistically, the differential input impedance of the op-amp itself (1 MΩ to 1 TΩ), multiplied by the open-loop gain of the op-amp) Due to the strong (i.e.,
unity gain) feedback and certain non-ideal characteristics of real operational amplifiers, this feedback system is prone to have poor
stability margins. Consequently, the system may be
unstable when connected to sufficiently capacitive loads. In these cases, a
lag compensation network (e.g., connecting the load to the voltage follower through a resistor) can be used to restore stability. The manufacturer
data sheet for the operational amplifier may provide guidance for the selection of components in external compensation networks. Alternatively, another operational amplifier can be chosen that has more appropriate internal compensation. The input and output impedance are affected by the feedback loop in the same way as the non-inverting amplifier, with
B=1.
Summing amplifier A summing amplifier produces the negative of the sum of several (weighted) voltages: : V_{\text{out}} = -R_{\text{f}} \left( \frac{V_1}{R_1} + \frac{V_2}{R_2} + \cdots + \frac{V_n}{R_n} \right) • When R_1 = R_2 = \cdots = R_n, and R_{\text{f}} independent : V_{\text{out}} = -\frac{R_{\text{f}}}{R_1} ( V_1 + V_2 + \cdots + V_n ) \! • When R_1 = R_2 = \cdots = R_n = R_{\text{f}} : V_{\text{out}} = -( V_1 + V_2 + \cdots + V_n ) \! • Input impedance of the '''
nth''' input is Z_n = R_n (V_- is a
virtual ground)
Instrumentation amplifier Combines very high
input impedance, high
common-mode rejection, low
DC offset, and other properties used in making very accurate, low-noise measurements • Is made by adding a
non-inverting buffer to each input of the
differential amplifier to increase the input impedance. ==Oscillators==