Operational amplifiers (op-amps) are analog circuit components that require power to operate. They are widely used in amplification and signal-conditioning circuits.

The symbol for an op-amp is shown in Figure 1. The symbol is a triangle, with two leads drawn on one side of the triangle, and the third lead is drawn at the apex opposite to that side.

One lead is defined as the inverting input (-), the other lead is defined as the non-inverting input (+), and the third lead is the output. The voltages at these two inputs and at the op-amp output are referenced to the ground.

Figure 1 also shows the connections for the positive and negative supply voltages, although these connections are normally omitted when an op-amp is drawn in a circuit. The supply voltage is typically ±15 V.

There are two other connections to the op-amp (called the balance or null offset) that permit adjustment of the op-amp output, but they are typically not shown.

# Op Amp | Operational Amplifier Basics

Commercially, op-amps are available in a variety of forms. A common form is the single op-amp in the form of an 8-pin integrated circuit (IC), an example of which is the LM741 chip from National Semiconductor. The pin-layout of this chip is shown in Figure 2(a).

**Note that** there is no connection to pin 8, and the positive and negative supply voltages are connected at pins 7 and 4, respectively.

Another form is the dual op-amps on a single 8-pin package, and the pin layout for this form is different than that of single op-amp IC. Many vendors manufacture op-amp ICs, and they are available in other chip numbers such as the LF411 chip that is also available from National Semiconductor.

An op-amp is constructed from a number of components including transistors, diodes, capacitors, and resistors.

An ideal op-amp can be modeled as shown in Figure 2(b). The inputs to the op-amp can be thought to be connected internally by a high-impedance resistor R_{in}. The value of this resistance is high enough (more than 1 M Ω), such that for ideal behavior, we can assume that no current flows between the V_{–} and V_{+} input terminals.

The output of the op-amp is modeled as a voltage source connected to a low impedance resistor R_{o} (less than 100 Ω) in series.

The voltage output is proportional to the difference between the input voltages, i.e.,

V_{o} = K_{OL} x (V_{+} – V_{–})

where K_{OL} is the open-loop gain of the op-amp. The open-loop gain of the op-amp is usually very high (10^{5} to 10^{6} ), so a very small voltage difference between the two inputs results in a saturation of the output.

For example, if the gain is 10^{6} , and the saturation voltage is 10 V, then the op-amp will saturate if the voltage difference between the input leads exceeds 10 µV.

Since the op-amp output is finite, but the op-amp has a very large gain, we assume that V_{+} = V_{–}. The assumption that V_{+} = V_{– }along with the assumption that no current flows into the input terminals are the two basic rules that are used to analyze ideal op-amp circuits.

It should be noted that the saturation voltage of an op-amp is a function of the supply voltage for the op-amp and it is slightly smaller than it. For example, at supply voltage of ±15 V, the saturation voltage is about ±13 V.

The open-loop input output relationship for an op-amp is shown in Figure 3.

In most cases, however, op-amps are not used in open-loop configuration but are used with a feedback loop between the output voltage lead and the inverting input lead. The closed-loop gain is much smaller than the open-loop gain, but the feedback provides more stable operating characteristics.

**Note that** an op-amp gives a zero output if the two input voltages are the same. This is called the common-mode rejection property of the op-amp. In reality, the output will not be exactly zero, but one can use the null offset terminals on the op-amp to adjust this output.

Op-amps have good frequency response characteristics, and their bandwidth exceeds 1 MHz. Op-amps can perform various operations such as comparison, amplification, inversion, summation, integration, differentiation, or filtering.

The particular operation depends on how the op-amp is wired and what external components are connected to the op-amp. We will discuss below some of these operations assuming ideal behavior. In most cases, the real-behavior closely follows the ideal behavior.

## Comparator OP-AMP

A comparator is used to compare two voltage signals, and switch the output to +V_{sat} if one of the signals is larger than the other, and to -V_{sat} otherwise, where V_{sat }is the saturated output of the op-amp. The circuit for an op-amp operating as a comparator is shown in Figure 2.27.

Here the op-amp is operating in open-loop, which means there is no feedback from the op-amp output to the input. The input voltage V_{i} is connected to the non-inverting input (+), and the reference voltage V_{ref} is connected to the inverting input (-). The comparator output V_{o} is then

A comparator can be used, as an example, in situations where it is needed to set an output on if a sensor input exceeds a certain value.

## Inverting OP-AMP

The inverting op-amp circuit is shown in Figure 4 which has a feedback loop between the op-amp output and the inverting input (-).

An input voltage V_{i} is applied to the inverting input through a resistor R_{1}, and the non-inverting input (+) is grounded. Since the non-inverting input is connected to ground,

V_{–} = V_{+} = 0

The current I_{1} is equal to I_{2} because virtually no current flows between the inverting and the non-inverting inputs. The current I_{1} is equal to

I_{1} = (V_{i} – V_{–})/R_{1} = V_{i}/R_{1}

and the current I_{2} is equal to

I_{2} = (V_{–} – V_{o})/R_{2} = -V_{o}/R_{2}

Equating I_{1} to I_{2}, and solving for the op-amp output V_{o} gives

V_{o} = -R_{2}V_{i}/R_{1}

Thus in this circuit the op-amp inverts the input voltage and amplifies it by a factor equal to the ratio of the resistance of R2 to R_{1}.

An application of this circuit is to perform signal inversion where the output will have a 180° phase shift with the input.

## Non-inverting OP-AMP

The non-inverting op-amp circuit is shown in Figure 5. Here the non-inverting input (+) is connected to an input voltage V_{i}, and the inverting input (-) is connected to ground through a resistor R_{1}. There is also a feedback loop between the op-amp output and the inverting input.

The voltage V_{+} is equal to V_{–} and is also equal to V_{i} in this case. But the voltage at the inverting input is also given by

since R_{1} and R_{2} act as a voltage-dividing circuit between V_{o} and ground. Thus, the output V_{o} of the op-amp is given by

Notice how the gain of the op-amp in this case is always greater than 1.

Now if we let R_{2} to be zero and R_{1} to be infinite, this gives the circuit shown in Figure 6. This circuit is known as a **voltage follower** or buffer, and V_{o} = V_{i} in this case.

Because the op-amp has a low output impedance (about 75 Ω), and a high input impedance (about 2 M Ω), the voltage follower circuit can be used in a variety of ways to reduce loading effects.

The output of a voltage source can be connected to the buffer input to isolate the source from the rest of the circuit, or the buffer output can be connected to a high-impedance circuit.

Note that in both the inverting and the non-inverting op-amp circuits shown above, the feedback between the output voltage and the inverting input is known as negative feedback. Negative feedback results in a linear relationship between the output and input voltages.

If the feedback loop was between the output voltage and the non-inverting input, then the output-input relationship is nonlinear. The nonlinearity is a hysteresis where the input has to change by a certain amount before the output changes state.

Non-linear op-amp circuits are utilized in the design of **Schmitt triggers**, which are IC circuits that are used for converting slowly changing or noisy analog signals into two-level digital signals.

The symbol for a standard (non-inverting) Schmitt trigger and the input and output voltages from a Schmitt trigger are shown in Figure 7.

Note how the output of the Schmitt trigger goes to V_{max} when the input signal voltage exceeds the positive going threshold voltage (V_{T+}). The output signal stays at V_{max} until the input signal drops below the negative going threshold voltage (V_{T-}), at which point the output goes to V_{min}.

In Figure 7, V_{max }and V_{min} are the positive (typically 5 VDC) and the negative (typically 0 VDC) supply voltage, respectively, for the Schmitt trigger device.

The 74HC7014 IC has six non-inverting Schmitt triggers with V_{T+} = 3.1 V and V_{T-} = 2.9 V when used with a 5 VDC supply voltage.

## Differential OP-AMP

An op-amp circuit with two voltages (V_{1} and V_{2}) applied to its inputs is shown in Figure 8. Two inputs (differential input) are used to reduce the circuit sensitivity to noise, since any noise applied to the circuit will be most probably the same on each of the inputs.

For this circuit, the current through the R_{1} and the R_{2} resistors is the same, since no current goes through the inverting input. This current is given by

and shows that the output of this op-amp circuit is proportional to the voltage difference between the inputs V_{2} and V_{1}.

A differential amplifier circuit can be used, for example, to implement an analog proportional control feedback loop (see Figure 9).

If the reference signal V_{R} is the V_{2} voltage, the actual or measured signal V_{A} is the V_{1} voltage, and the ratio R_{2}/R_{1} is the proportional gain K_{p}, then the output of the differential amplifier will be

Another application of the differential amplifier circuit is to amplify the difference between the voltage outputs from the arms of a Wheatstone bridge used to measure strain.

## Integrating OP-AMP

The circuit for an integrating op-amp is shown in Figure 10, which has a capacitor C in the feedback loop.

The current through a capacitor is given by

I_{C} = Cdv/dt

For this capacitor V_{o} = V_{–} – V_{o} = -V_{o}, since V_{–} = 0. But the current through this capacitor is the same as the current that passes through the resistor R, since no current flows through V_{–}. This current is given by

where V_{o}(0) is the initial condition for the capacitor voltage. Thus, in this circuit, the op-amp produces an inverted output of the integral of the applied input voltage.

Note that if the capacitor and the resistor were interchanged in this circuit, the op-amp will act as a differentiator of the input signal.

The op-amp output in this case will be

V_{o} = -RC dv_{i}(t)/dt

Note that any noise in the input signal will be amplified by differentiation.

## Power Amplifier

A standard op-amp (such as the LM741) has a current output rating of about 25 mA. This is not sufficient to meet the current needs of driving loads (such as valve actuators, servo motors, and audio amplifiers).

Commercial op-amps with a higher current output rating are available. These op-amps are called power op-amps, an example of which is the OPA547 chip from Texas Instruments. The OP547 can provide a continuous output current of 500 mA with the ability to control the output current limit.

Power op-amps can be conveniently used to interface a digital-to-analog (D/A) converter that needs to drive a DC motor. Table 1 gives a sampling of power op-amp devices.

In Table 1, the ‘Power Supply Range’ column defines the allowable voltage levels that can be applied to the positive and negative supply inputs of the op-amp. The power supply range affects the op-amp output voltage swing, which is the maximum voltage that the op-amp can produce without saturation for a given load. Note that the output voltage swing is proportional to the power supply range.

The ‘Slew Rate’ column defines the rate at which the op-amp output voltage will change when the op-amp gain is set to unity. Several of the power op-amps listed in the Table 1 allow adjustment of the maximum output current of the op-amp.

Due to their large output current, power op-amps are available in packages with a built-in copper tab to allow easy mounting to a heat sink for good thermal performance.