Having read this workbook you should be able to : define the open loop voltage gain of an amplifier,

Transcription

1 Ojectives Having read this workbook you should be able to : define the open loop voltage gain of an amplifier, state why negative feedback is often used in amplifiers, describe the function of operational amplifiers in terms of its two inputs and output, define, and illustrate, the term saturation, state the properties of an ideal operational amplifier and compare with real properties, derive the gain formula for inverting, and noninverting, voltage amplifiers, indicate the value of input impedance for inverting, and noninverting amplifiers, describe, and illustrate, the use of inverting, and noninverting, amplifiers for AC amplification. 1

2 ANALOGUE SYSTEMS In our study of digital circuits we dealt with signals where the voltages could only take one of two values (high or low). In analogue systems, voltage signals within the system can take any value between a maximum and a minimum. Voltage amplifiers form basic processing units in analogue circuits. At this stage we are interested in the function of such units only and shall not be considering how they are made up. Fig 1 shows the symbol used to represent a voltage amplifier. Power supply connections are not shown on the diagram. A o Fig. 1 The input signal is applied across the input terminal and the line while the output is obtained across the output terminal and the line. A voltage amplifier produces an output voltage which is a larger version of its input voltage i.e. the output voltage is proportional to the input voltage. The open loop gain (A o ) of the amplifier is given by : A o = Before introducing operational amplifiers we shall define a few terms that are often used when considering amplifiers. 2

3 NEGATIVE FEEDBACK An amplifier with a high gain tends to be rather unstable i.e. its gain is affected by changes in temperature or small changes in supply voltage. It can be made more stable by applying negative feedback. Negative feedback means feeding back part of the output signal to the input in such a way as to effectively reduce the input signal. Suppose a fraction b of the output voltage signal is fed back to the input. b is called the feedback factor. b A o b. Fig. 2 Amplifier with negative feedback. The effective signal at the input of the amplifier is now ( b. ). You should be able to show that: Gain with feedback = A = = A o 1 ba o The equation shows that applying negative feedback reduces the effective gain of an amplifier. This is more than made up for by increased stability and bandwidth. 3

4 OPERATIONAL AMPLIFIERS (Opamps) Operational amplifiers were originally designed to perform mathematical operations in analogue computers. They have two inputs and amplify the difference in voltage between the two inputs. A 741 operational amplifier, the type used in the practical exercise, has an open loop gain of about Fig 3 shows the pin connections for the 8pin DIL 741 package. V s V s OFFSET OFFSET V s inverting input noninverting Fig. 3 Pin connections (741) The diagram shows that a 741 requires a positive (V s ) and a negative (V s ) voltage supply. Such a supply is called a dual power supply. The 741 will work on a dual supply providing a voltage of between ±5V and ±15V. Fig 4 shows how such a supply is connected to the 741. Power supply connections will not be shown on future diagrams. Vs POWER SUPPLY 15V 15V Vs Fig 4 Power Supply connections NB Input signals are applied across the input pins and the line while the output is available across the output pin and the line. The line may not always be directly connected to the opamp. 4

5 THE INVERTING AND NONINVERTING INPUTS The inputs are referred to as the inverting input () and the noninverting input (). The negative and the positive signs have nothing to do with the power supply polarity and should not be referred to as the positive input and negative input. If the two inputs are connected together, there is no difference in voltage between the two inputs. The output should be at. If the noninverting input is more positive than the inverting input, the output will be positive. If the inverting input is more positive than the noninverting input, the output will be negative. Fig. 5 If the voltage at the noninverting input is V () and the voltage at the inverting input is V (), then: = A 0.(V () V () ) where A 0 is the openloop gain of the amplifier. Output at Output Positive Output Negative OFFSET Opamp packages are mass produced and sometimes we find that is not zero when V () = V (). Pins are provided on the package which enable us to null this offset. PIN 1 10k V S PIN 5 Fig. 6 5

6 GAIN AND SATURATION The output voltage cannot move outside the range of the power supply. If the difference in voltage between the inputs is very small, the output voltage will be A o times the difference. If the difference is increased, a point will be reached when the output voltage cannot increase further and the amplifier becomes saturated. V s Saturation (V () V () ) Saturation V s Linear region Fig. 7 When operated on a ±15V supply, a 741 saturates when the output voltage reaches about ±13V. PROPERTIES OF AN IDEAL OPERATIONAL AMPLIFIERS 1. An ideal operational amplifier has infinite gain. 2. An ideal operational amplifier has infinite input resistance and draws no current at its input. 3. An ideal operational amplifier has zero output resistance. 4. An ideal operational amplifier has an infinite bandwidth. 6

7 USES OF OPERATIONAL AMPLIFIERS A. INVERTING VOLTAGE AMPLIFIER An operational amplifier would be very unstable if used for voltage amplification at full openloop gain. A resistor chain can be used to provide negative feedback. Fig 8 shows the arrangement used to form a defined gain inverting voltage amplifier. I 2 R f I 1 R in A Fig. 8 Inverting voltage amplifier In deriving the gain formula for the inverting voltage amplifier we shall be making two assumptions. If the amplifier is not saturated, the voltage difference between the noninverting and the inverting input is very small. The noninverting input is connected to. Assuming infinite gain, the voltage at point A can also be taken as. Point A is said to be a virtual earth point. and I 1 = 0 = R in R in I 2 = 0 = R f R f 7

8 If we assume infinite input impedance, no current will flow into the amplifier at the inverting input. Therefore: I 1 = I 2 Therefore: = R f R in Voltage gain (A) = = R f R in The negative sign indicates that if the input is taken positive the output becomes negative. NB The overall gain is not dependent upon the gain of the operational amplifier. The gain depends upon the values of the external components only. The input impedance to the amplifier is equal to the value of R in. This will often be low (<10kΩ) and introduces an undesirable feature into the system. AC VOLTAGE AMPLIFICATION If an alternating voltage is applied at the input of an inverting amplifier, the output voltage will also be alternating but 180 o out of phase with the input. (Fig 9) time time Fig. 9 Inverting action AC amplification will be investigated further during the practical session. 8

9 B. NONINVERTING VOLTAGE AMPLIFIER Fig 10 shows how an operational amplifier can be set up as a noninverting voltage amplifier. R f A I 1 I 2 B R 1 Fig 10 Noninverting voltage amplifier The high gain of the operational amplifier means that, if the amplifier is not saturated, points A and B can be considered to be at the same voltage., i.e. V A = V B = Point A is not a virtual earth in this case. Assuming infinite input impedance : I 1 = I 2 = I Applying Ohm s law to resistors : V A = = I.R f... (1) V A 0 = 0 = I.R 1... (2) Dividing equation 1 by equation 2 : Note that: = I.R f I.R 1 Gain = = R f 1 R 1 The input signal is applied across the noninverting input and. The input impedance is that of the opamp itself (infinite in theory). It is not possible to obtain a gain of <1 with this arrangement. 9

10 DESIGN NOTES There are a number of design rules that should be followed for both inverting and noninverting amplifiers. 1. All resistors must be in KΩ 2. The input resistance of an inverting amplifier is Rin and a noninverting amplifier is the impedance of the opamp. 3. The gain is set by the ratio of resistors only. An inverting amplifier has a Gain = R f /R in If a gain of 24 is required there are 2 unknowns 24 = R f /R in The negative signs can be removed, therefore: 24 =R f /R in Rearranging by multiplying both sides by Rin gives: 24 R in = R f If no values are given, a good rule is to make R in = 10KΩ, in this example R f would be 240KΩ. An inverting amplifier has a Gain = R f /R 1 1 This again can be rearranged to produce ratios. The equation becomes: Gain 1 = R f /R 1 Multiply both sides by R 1 : R 1 (Gain 1) = R f If a gain of 5 is required, the ratio is 4 : 1. If no resistor values are given, use the rule that the smallest resistor is 10KΩ, R f would be 40KΩ and R 1 would be10kω. 10

11 1. Which one of the following is correct? An ideal operational amplifier input has: A B C D zero input impedance and infinite gain. infinite input impedance and zero gain. infinite output impedance and infinite gain. infinite input impedance and infinite gain. R f R in The above diagram is used with questions If R in = 10kΩ and R f = 47kΩ, the theoretical value of the voltage gain is: A 4.7 B 47 C 4.7 D If R in = 10kΩ and R f = 47kΩ, the output voltage for an input voltage of 0.25V will be about: A 1.2V B 1.2V C 0.05V D 0.05V 11

12 4. If R in = 10kΩ and R f = 1kΩ, the theoretical value of the voltage gain is: A 10 B 10 C 0.1 D If R in = 100kΩ and R f = 1kΩ, the theoretical value of the output voltage for an input voltage of 5V is: A 50mV B 5mV C 50mV D 5mV R f R 1 The above diagram is used with questions 10 and If R 1 = 10kΩ and R f = 47kΩ, the theoretical value of the voltage gain is: A 4.7 B 5.7 C 4.7 D If R 1 = 10kΩ and R f = 100kΩ, the output voltage for an input voltage of 0.25V will be about: A 2.75V B 2.75V C 2.5V D 2.5V 8. If R 1 = R f = 10kΩ, what is the value of the voltage gain provided? Remember to enter or before the value.. 12

13 Exercise Objectives Having completed this Exercise you should be able to: set up an opamp as an Inverting Voltage Amplifier. plot the transfer characteristics for an Inverting Voltage Amplifier. use the transfer characteristics to measure the gain and saturation level for an Inverting Voltage Amplifier. investigate how saturation depends upon supply voltage. investigate the performance of an Inverting Voltage Amplifier when an AC signal is applied at its input. set up an opamp as a Noninverting Voltage Amplifier. investigate the performance of a noninverting voltage amplifier when an AC signal is applied at its input. EQUIPMENT REQUIRED DIGITAL MULTIMETER CATHODE RAY OSCILLOSCOPE FUNCTION GENERATOR 13

14 ACTIVITY 1 In this Activity you will be investigating an inverting voltage amplifier. 1a. Set up the circuit shown below, set the supply voltage to ±12V A 5V 5V 10k 1k We are now ready to set voltages at the input of the inverting voltage amplifier and measure the resulting output voltages. This can be done using a Cathode Ray Oscilloscope (CRO) or a digital multimeter. Your tutor will tell you which you should use. USING A CRO The following instruction apply to a Hameg 2035 but will be very similar for other models. a. Select DUAL then set the time base (Time/div) to about 1ms/div. This provides a steady trace across the screen. Channel 1 is used for monitoring the input voltage. Set its ground level at the bottom of the screen then select a sensitivity of 0.1V/div. Channel 2 is used for monitoring the output voltage. Set its ground level at the top of the screen then select a sensitivity of 1V/div. b. Connect the ground clips on the CRO probe leads to the line. Connect Channel 1 probe tip to the output of potentiometer A and Channel 2 probe tip to. Sensitivity for both channels will have to be changed at higher values of. If you have any doubt, consult your tutor. USING A DIGITAL MULTIMETER A digital meter set to suitable DC voltage ranges can be used to monitor input and output voltage. The black (COM) lead should be connected to the line. 14

15 Adjust potentiometer A so that 0.1V is provided at the input of the inverting voltage amplifier. Record the value of the output voltage in the table provided below. Remember to indicate whether it is or. INPUT VOLTAGE OUTPUT VOLTAGE VOLTAGE GAIN ( ) ( ) / 0.1V 0.2V 0.4V 0.6V V 2. Repeat for other values of input voltage. Set the potentiometer to provide the negative voltage listed in the following table. Record the value of the output voltage in each case. INPUT VOLTAGE OUTPUT VOLTAGEVOLTAGE GAIN ( ) ( ) / 0.1V 0.2V 0.4V 0.6V V 2. Plot a graph of against. 15

16 ACTIVITY 2 We shall now investigate the action of an inverting voltage amplifier upon an AC signal. 2a. Set up the following arrangement. 10k 1k 2b. Set the supply voltage to ±12V. 2c. Connect a Function Generator across the input of the amplifier and. Set the Function Generator to provide a sine wave output of peak value 0.5V and frequency 1kHz. 2d. Use a CRO to investigate the input and output signals. Complete both of the following graphs, clearly indicating the value of the peak voltages. Input voltage time(ms) Output voltage time(ms) Calculate the value of the AC voltage gain. 16 Voltage gain at 1kHz =.

17 2e. Increase the peak value of the input voltage to 2V. Complete the following graphs by showing the output voltage obtained. Input voltage time(ms) Output voltage time(ms) 2f. Determine the value of the peak input voltage at which clipping starts to occur. 17

18 ACTIVITY 3 In this activity you will be investigating a noninverting voltage amplifier. 3a. Set up the following arrangement with the Supply Voltage at ±12V. R f 10k R 1 1k 3b. Connect the noninverting input to potentiometer A and set the input voltage to 0.5V. Record the value of the output voltage. Output voltage =. 3c. Replace the 1kΩ resistor (R 1 ) with a 27kΩ resistor. 3d. Measure the output voltage for an input voltage of 0.5V. Output voltage =. Calculate the value of the voltage gain. Voltage gain =. 18

19 3e. Remove the connection between the noninverting input and potentiometer A and set up the arrangement as in 3a (R 1 = 1kΩ). 3f. Connect a Function Generator, set to provide a sine wave of peak value 0.5V and frequency 1kHz, across the input and. 3g. Complete the following graphs by showing input and output voltage. Input voltage time(ms) Output voltage time(ms) 3h Calculate the AC voltage gain. Voltage gain =. 19