v 0 = A (v + - v - ) (1)

Transcription

1 UNIVERSITI TEKNOLOGI MALAYSIA KURSUS KEJURUTERAAN ELEKTRIK ELECTRONIC ENGINEERING LABORATORY 2 EXPERIMENT 2 : OPERATIONAL AMPLIFIER PRELIMINARY REPORT Name : Section : Group : Lecturer : Marks : 20 Attach this preliminary report together with your laboratory report. THEORY : OPERATIONAL AMPLIFIER An operational amplifier (op-amp) is a device with two inputs and a single output. The output of the amplifier v 0 is given by the formula: v 0 = A (v + - v - ) (1) Where A is the open-loop voltage gain of the amplifier, v + is the non-inverting input voltage and v - is the inverting input voltage. Both v + and v - are node voltages with respect to ground. Typically, the open-loop voltage gain A is on the order of A resistor is placed between the output node and the inverting input to provide feedback and adjust amplification. When an op-amp circuit behaves linearly, the op-amp adjusts its output current such that the voltage difference between the two inputs is nearly zero. v - = v + (2) Another important feature of the op-amp is that its input resistance is very large and may be taken as infinite in many applications. The most common type of op-amp is the which as an input resistance of 2 MΩ. This is large enough to be considered infinite in most applications. Because of the high input resistance, only a very small current flows into either input of an op-amp. In practical op-amp circuits, the current flowing into either of the inputs is usually on the order of µa. In the case of an ideal op-amp, where the single assumption is made that the open-loop voltage gain A goes to infinity, i i = 0 (3) Salmiah &Zaimah(June 06) 1

2 where i i is defined to be the current entering the non-inverting input and exiting the inverting input. Equations 2 and 3 can be used to analyze most of the properties of opamp circuits. Figure 1 shows an operational amplifier with an open-loop voltage gain A. The terminals labeled + Vcc and - Vcc are power supply connections to the op-amp and set limits on the voltage which can be produced at the output node. Figure 2 shows the practical op-amp model and Figure 3 is the 8 pin DIP IC. V + V - i + i - +V CC -V CC V - + 2MΩ + V Ω (V + - V - ) Figure 1 Figure 2 Figure 3 Salmiah &Zaimah(June 06) 2

3 Inverting Amplifier In Figure 4 is shown an op-amp in the inverting configuration along with the power supply connections + Vcc and - Vcc.. R 2 R 1 2 +V CC V S 3 - V CC R 3 Figure 4 To analyse this circuit, we will use Kirchhoff's Current Law to determine the output node voltage v o and the circuit voltage gain given by the formula voltage gain = v 0 / v s (4) To analyse an op-amp circuit we first look at the op-amp input nodes (2 and 3). Assuming an ideal op-amp, no current flows into either of the op-amp inputs ( Equation 3). The current through R 3 is zero and therefore v 3 = 0. From Equation 2 we know that v 2 = v 3 = 0, because op-amp circuit behaves linearly (v - = v + ). From this, the current flowing through resistor R 1 is i R1 = (v 1 -v 2 )/R 1 =(v S -0)/R 1 = v S /R 1 (5) From Equation 3 we know that: i R1 = i R2 = v S /R 1. i R2 = (0-v 0 )/R 2 = i R 1= v S /R 1 (6) -v 0 /R2 = v S /R 1 (7) v 0 = -v S (R 2 /R 1 ) (8) Salmiah &Zaimah(June 06) 3

4 To find the voltage gain (of the amplifier circuit), we need to divide the output voltage by the input voltage: Gain = v 0 /v S = -R 2 /R 1 (9) Note that the final voltage gain is negative, thus the name inverting amplifier. Effect of input bias current Practically, when there is no input to the op-amp, there is a small input bias current flowing into the input resulting in the output error voltage when it should be zero. The function of Resistor R 3, is to compensate the effect of input bias current. The compensation resistor value equals the parallel combination of R 1 and R F. Non-inverting Op Amp The basic configuration for a non- inverting amplifier is shown in Figure 5. The voltage gain for this circuit is 1+R 2 /R 1 it will be left to you as an exercise to verify this voltage gain. R 2 R V CC - V CC R 3 V S Figure 5 Salmiah &Zaimah(June 06) 4

5 Slew rate Slew rate of an op-amp is a measure of how fast the output voltage can change in response to an input signal. The slew rate of the ua is 0.5 V/µs (typical). Figure 6 shows a step input, Vi and the ouput response of an op-amp circuit. V i V o dv o dt Figure 6 Slew rate, SR is the maximum rate at which an op-amp can change output without distortion. The slew rate is expressed as ΔVo SR = Δt V/µs (10) Since frequency is related to time, the slew rate can be used to determine the highest operating frequency of the op-amp without distortion as follows: f max SR = 2πVp (11) where V P is the peak voltage. Op amp as a comparator The purpose of the comparator is to compare two voltages and produce a signal that indicates which voltage is greater. Figure 7 shows an op-amp as a comparator. Since the voltage gain, A, of an op-amp is very large, any difference will be magnified to the power supply rails ± Vcc. If v S1 is greater than v S2 then the difference v + - v - will be positive and the result will be amplified to + Vcc. If, however, v S2 is greater, then the difference is negative and the result will be amplified to - Vcc. Finally, if the two voltages are exactly equal, then the difference will be zero and the output will also be zero. Salmiah &Zaimah(June 06) 5

6 +V CC 2 V S2 3 V S1 - V CC Figure 7 PRELIMINARY WORK 1 a) Verify that the voltage gain (v o /v s ) for the circuit in Figure 5 is 1+R 2 /R 1. Make use of the two op-amp virtual earth rules ( i + =i - = 0, v + = v - ). b) What value of feedback resistor R 2 is needed to give an amplification equal to 6 when R 2 =100 kω? c) What is the maximum supply voltages (±Vcc) for the op-amp, from the given data sheet? 2. a) What is slew rate? b) What is the value the op-amp slew rate from the given data sheet? c) From the value of the slew rate, calculate the maximum operating frequency for the op-amp, if V p = 10V. d) Given the output voltage of a step input to an op-amp circuit as in Fig 8, calculate the slew rate. V O 5mV 3 µs 10 µs t Figure 8 Salmiah &Zaimah(June 06) 6

7 3. Name the circuits below. What is the output voltage of each circuit 2V +10V 2V +10V 2V +10V - 10V - 10V - 10V ( a ) ( b ) ( c ) Figure 9: Op-amp circuits 4. In Figure 7, if v S1 is a sine wave voltage of 5 V peak-peak and v S2 is 2 V dc as shown in Figure 11, sketch the output voltage of the circuit with reference to the input voltages. Assume supply voltage (±Vcc) is ±10V. Figure 10 Salmiah &Zaimah(June 06) 7