Operational amplifiers (op amps) may initially look intimidating, but with a bit of study, they can be easily understood and used in a variety of applications.
Op amps can be thought of as a perfect amplifier in a black box. When we create a design using an op amp, we initially presume that the device has infinite gain and frequency response, infinite input impedance, zero output impedance, no input bias current, and no input offset voltage. None of the former specifications is true, but they come close. As a design engineer, you must work within those limits.
As a starting point, consider an amplifier made with individual transistors. It has a single input port and a single output port (see Figure 1). The input is applied to J1, and the output is taken at J2. The gain from input to output is a function of the current gain (beta) of the individual transistors, which means that if you built a number of these (e.g., on a production line), you would see gain variations.
Now, consider an amplifier built with an op amp. Referring to Figure 2, the first significant difference we notice with the op amp concerns its input structure – there are two inputs, one positive and one negative.
An op amp is a specialized type of amplifying device that falls within the broad category of servo amplifiers. Servo-amps accept an input signal and compare it to another signal, usually an attenuated version of the servo-amp’s output. The servo-amp then adjusts the output so that the attenuated output matches the input. The most important aspect of this action is a significant reduction in error voltages or signal distortion during amplification. The op amp is often powered from bipolar supplies (positive and negative), so it can amplify signal voltages centered around ground or the circuit’s common bus. See below for some further thoughts on the power supplies.
How it works
A signal present at the positive input will appear at the output in phase with the input. A signal present at the negative input will appear at the output 180° out of phase with the input. The input structure of the op amp mathematically subtracts the negative input signal from the positive input signal and then amplifies that difference by a high-gain stage. This mathematical difference circuit is typical of a servo amp when operated as a closed-loop servo system.
The very high gain might seem like it would create a lot of distortion, but by adding negative feedback around the op amp, this apparent shortcoming is easily addressed and turned into an advantage. With an attenuator network made up of just two resistors, the overall gain drops from very large to the mathematical inverse of the attenuation factor of the two resistors. Referring to Figure 3, the attenuation factor (alpha or α) is simply the voltage divider formula:
Therefore, the amplifier voltage gain (Av) is calculated as follows:
With some algebraic manipulation, we can rewrite this as:
For example, if RFB was 9.00 kΩ and RI was 1.00 kΩ, α would be 0.100, and Av would be 10.00 V/V (volts per volt). If the voltage at VIN were 1.00 V, the output voltage would rise until it was 10.0 V, at which point the voltage at the negative input would be 1.0 V. Thus, with the two voltages equal, the system is stable, and the output copies the input but increased by a factor of ten.
Besides the low distortion characteristic of this circuit, there is another important advantage: Compared to the circuit in Figure 1, if you build several of these amplifiers, the gain variation can be controlled as tightly as the tolerances of the two resistors.
These op amp gain blocks can be used to add multiple signals or voltages (both ac and dc offset voltages) together. They can also be tailored to have frequency-selective behavior. This is the heart of low-pass, high-pass, band-pass, and notch filters. We will take a closer look at filters in a later installment.
Power supply considerations
Note that in the op amp shown in Figures 2 and 3, there are both positive and negative power supplies, whereas the circuit in Figure 1 uses just a positive supply. The circuit in Figure 1 is typical of an ac amplifier, such as an audio preamp or power amp. The signal is capacitively coupled to the amplifier’s input and output. Any dc component presented to the input is blocked. Any dc component present around each transistor is just there to establish the quiescent operating point needed to put the transistor in its active operating region.
Consider a data-acquisition system. Some typical architectures might consist of sensors whose output is very low-frequency ac or slowly changing dc of either polarity. Examples of such sensors include thermocouples, photodetectors, accelerometers, and electrochemical cells. The outputs of these sensors must be amplified and possibly level-shifted (i.e., a dc offset added) before being sent to an analog-to-digital converter (ADC). For this, you will want to directly couple (instead of capacitively couple) the signals at the amplifier’s input and output.
By using op amps powered from a bipolar supply and ground-referencing the sensor signals, the op amp’s output will be at zero volts (ground) with no signal present. It can swing positive or negative as needed in response to the sensors. Such an amplifier chain can have overall stability and have a well-controlled amplification factor.
Now, consider combining some of the features of the previous designs. How should we proceed with, for example, an audio amplifier intended as a microphone preamp? The audio can be AC-coupled (both input and output); one or two op amps can provide sufficient gain. We want to power the amplifiers, as shown in Figure 1, with a single positive supply. It doesn’t seem like we need bipolar supplies, but we will need to add a dc offset to the op amps so that, with no signal present, their outputs are approximately halfway between the positive supply voltage and ground. Then, the signals can swing above and below this halfway or quiescent operating point.
You can easily do this with just a few passive components. Figure 4 shows a real-world circuit. For this circuit, I’ve chosen a specific supply voltage that is typical for such an application. I’ve also added a power supply bypass capacitor (C9). Supply bypass capacitors are always a good idea for op amp circuits, providing a low-impedance supply voltage and keeping things stable. I’ve also added R11 and R12, a simple 50% voltage divider which creates a half-supply voltage reference (+6V). Again, a bypass capacitor (C8) is added to keep the +6V node stable. R13 provides a dc return for the bias current present at the op amp’s positive input. R10 sets the gain (it’s equivalent to Ri in Figure 3) and provides a dc return for the bias current present at the op amp’s negative input.
As far as the input signal and ac gain calculations are concerned, the +6V node appears to be at ground. But if you built this circuit and placed a dc voltmeter at the op amp’s output, you would measure 6 V dc. Then, with an input connected, the output signal would ride on top of the steady-state 6 V dc.
When designing with op amps, there are more details to consider, such as the bias current mentioned above, input offset voltage, frequency, phase response, and output drive capability. We’ll take another look at those in subsequent articles.
