EEM 328 ELECTRONICS LABORATORY EXPERIMENT 1

OPERATIONAL AMPLIFIER CHARACTERISTICS

PURPOSE The purpose of this lab is to study the characteristics of the operational amplifier. Some of the characteristics that will be investigated include offset voltage, gain-BW product, and open-loop gain. THEORY Operational Amplifier An operational amplifier (or op-amp) is a high gain amplifier which is usually powered using equal but opposite polarity voltage sources. The symbol and the circuit model can be seen in Figure 1.

Figure 1: Symbol and circuit model for an op-amp

As it can be seen, the amplifier takes the difference between the two input signals and amplifies it by a factor of Aod. vo = Aod (v2 – v1) = Aod vd Rin represents the input impedance and Rout represents the output impedance of the amplifier. An ideal op-amp amplifier has the following ideal characteristics: - Input Resistance is infinite. - Output resistance is zero - Open-loop voltage gain, Aod, is infinite - Bandwidth is infinite - vo=0 when V2 = V1 Because of these parameters, the op-amp is designed to be used in a feedback loop rather than as a stand alone (open-loop) device. This means that in a practical op-

amp circuit, there is usually an external path which feeds some of the output of the op-amp back into its input. The parameters of an actual opamp such as the 741 differs from the ideal op-amp. Table 1 shows these differences. Parameter Ideal General Purpose 741 Op-Amp Voltage Gain, G Infinite 105 Output Impedance, Ro 0 75 Ω Input Resistance, Rin Infinite 2 MΩ Offset Current, Iio 0 20nA Offset Voltage, Vio 0 2mV Bandwidth, BW Infinite 1 MHz Slew Rate, SR Infinite .7 V/µs

Table 1: Comparison of the parameters of an ideal op-amp to a real op-amp (741)

The parameters which characterize the op-amp can be described in the following manner. Input and Output Resistances, Rin and Ro The input resistance looking into the two input terminals of the op-amp is ideally infinite. This means that the device draws no current. For a real 741 op-amp, the input resistance is about 2MΩ. For FET op-amps, this resistance can be much higher (1012 Ω). The output resistance on the other hand is ideally zero. For the 741, it is about 75 Ω. This makes the op-amp ideal for driving low resistance loads. Open Loop Gain, G This is the gain of the op-amp if a signal is fed differentially into the input of the amp and no feedback loop is present. This gain is ideally infinite, but in a real op-amp the maximum gain is finite (about 105 ) . The gain also depends strongly on frequency. For low frequency inputs it takes on its maximum value, but the gain decreases rapidly as the input frequency goes up. For a 741, the gain decreases to 3dB (2^0.5/2) of its maximum value at 1MHz. Input Offset Voltage, Vio When the difference between the two input signals is zero, ideally the output is zero also. However, in a real op-amp, because of manufacturing methods, this is not the case. For a 741, the output voltage when vd = 0 is about 2mV. This can be measured by tying both inputs of the amplifier to ground and measuring the output voltage. This is the output offset voltage. This voltage is then divided by the open-loop gain of the device to get the input offset voltage.

Input Offset Current, Iion Because the ideal op amp has an infinite input resistance, it draws no current (it looks like an open circuit). Each input draws a small amount of current. The difference between the amount of current drawn into the positive and negative input terminals is called the input offset current (Iio = IB+ – IB-). This can cause errors in the output voltage. Gain - Bandwidth Product As mentioned before, the gain of the op-amp is frequency dependent. The frequency response of the open loop gain is such that the frequency decreases with gain. By looking at the graph in Figure 2, it can be seen that the op-amp displays the property that the open-loop gain times the frequency is a constant. This constant is defined as the gainbandwidth product and it is 1 x 106 for the 741 amplifier.

Figure 2: Frequency versus Open Loop Gain for a 741 Op-Amp

Slew Rate An ideal op-amp has an infinite frequency response. This means that no matter how fast the input changes, the output will be able to keep up. In a real op-amp, this is not the case. If the input signal changes too fast then the output will not be able to keep up. This is defined as slewing and it results in distortion of the output waveform. Stated more formally, Slew Rate = SR = maximum dvo/dt or the maximum rate at which the output can change without distorting. This can be measured by applying a high frequency square wave signal. The frequency of the waveform should be increase until the waveform becomes a triangular wave. The slope of the triangular waveform is the slew rate. (SR = ∆V/∆T) PRE-LAB

1) Study the circuit model of operational amplifiers.

2) Find the transfer functions Av=vout/vin for circuits in Appendix Figures 1-7. Using the explanations given in the next section, study the operation of the circuits. PROCEDURE The 741 op-amp is an 8 pin chip. The pin-out for this chip can be seen in Figure 3. This chip is typically powered using ±15V supplies on pins 7 and 4.

Figure 3 The pin-out for the 741 Op-Amp

Connect the following circuits: 1) Comparator (Appendix Fig. 1). Apply a 1 kHz sine wave signal of about 1 volt p-p to the noninverting (+) input, with the inverting (-) input grounded. Observe this signal on the oscilloscope, triggering on external. Sketch the output. 2) Follower (Appendix Fig. 2). Apply the same signal to the input as in part (1). Note that with negative feedback (to the inverting input) the op-amp adjusts its output so that the inverting input is at the same voltage as the noninverting input. 3) Non inverting amplifier (Appendix Fig. 3). The two 1 kΩ resistors divide the signal at the output of the amplifier by a factor of two. In order for the voltages at the two inputs to the amplifier to be equal the circuit must have a gain of two. Apply the same signal as in part (1) to the input. 4) Inverting amplifier (Appendix Fig. 4). In this circuit the noninverting input is at ground. In order to keep the inverting input near ground the amplifier must "balance" a positive input with a negative output, and vice versa. Measure the voltage at the inverting input. The inverting input is said to be at a "virtual ground." Observe the performance of the amplifier on the oscilloscope. The input impedance of a circuit is the ratio of the input voltage to the input current. With a 1 volt input, calculate the current flowing through the 1 kΩ input resistor.

5) Differentiator (Appendix Fig. 5). This circuit differentiates the input voltage. Since the inverting input is at a virtual ground, the current flowing through the 1 kΩ resistor, and hence the output voltage, is proportional to the derivative of the voltage across the 0.2 µF capacitor.

Apply the same signal as in part (1) to the input. (Careful – be sure to trigger the scope on external or you may miss the 90o phase shift!) 6) Integrator (Appendix Fig. 6). In this circuit the capacitor and the resistor are interchanged and the signal is integrated instead of differentiated. In addition, a 100 kΩ resistor has been added to prevent any input offset voltage that might be present from driving the output of the op-amp to one of its extreme limits. Apply the same signal as in part (1) to the input. Apply the same signal as in part (1) to the input. (Careful - be sure to trigger the scope on external or you may miss the 90o phase shift!) 6) Integrator (Appendix Fig. 6). In this circuit the capacitor and the resistor are interchanged and the signal is integrated instead of differentiated. In addition, a 100 kΩ resistor has been added to prevent any input offset voltage that might be present from driving the output of the op-amp to one of its extreme limits. Apply the same signal as in part (1) to the input. (Better trigger the scope on external again!) 7) D/A converter (DAC) (Appendix Fig. 7). The op-amp in this circuit is effectively an inverting amplifier with four separate inputs. Because the inverting input is held at a virtual ground, currents from the four inputs are added and flow together into the output resistor. The values of the four input resistors have been chosen so that each one causes approximately twice as much current to flow as the previous one. Measure the output voltage as a function of the digital input, using the following series: 0 0000 all inputs grounded 1 0001 1st input at 5 Volts 2 0010 2nd input at 5 Volts 3 0011 1st and 2nd inputs at 5 Volts ASSIGNMENT Using your measurements of the D/A converter, plot the output voltage (Y axis) as a function of the digital input (X axis). Draw a straight line fit to the data.

Appendix