Operational Amplifiers - Configurations and Characteristics What is an Op Amp An Op Amp is an integrated circuit that can be used to amplify both DC and AC signals. One of the most common Op Amps available is the LM 741. Inside the Op Amp is a complex electronic circuit. You can use the Internet to find a picture of the equivalent circuit of the Op Amp. The diagram below shows the pin numbers for the various terminals of the device. Note that the Op Amp requires plus and minus voltage sources to power the device. Op Amp Model The diagram shows a simplified model of an Op Amp. It consists of 2 inputs a Non-Inverting input V+ and an Inverting Input V-, an output V OUT, an input resistance R IN, an output voltage source GV IN and an output resistance R OUT. The values of these parameters for a LM 741 Op Amp are found in the table below. Parameter Value Input resistance 2 MΩ Output resistance 75 Ω Open loop gain -G 100,000 1
Open Loop Configuration The open loop gain was referred to in the model as G but it is also commonly designated as A OL. This is an extremely large value and makes the Op Amp an impractical amplifier in an Open Loop configuration. Like β for a bipolar transistor, the value of the open loop gain (A OL ) is highly variable from one device to another of the same type. Saturation Voltage The output voltage from an Op Amp circuit can only approach the value of the DC supply voltage(s). These are referred to as the saturation voltages and represent the maximum output voltage. V SAT = ± V CC (1 to 2 V) so for V CC = ± 12V the maximum outputs voltages are approximately ± (10 to 12) V. The plus and minus saturation voltages are typically not equal. Sample Calculation This calculation illustrates the difficulties with Open Loop mode. Assume A OL = 100,000 and V SAT = ± 10 V The minimum input voltage that will cause the output to saturate is V IN,min = ± 10 V/100,000 = ± 100 µv This is a very small input signal and makes the Op Amp not practical for larger input signals. This calculation illustrates one significant conclusion for Op Amps. The voltage difference between the 2 input terminals is essentially zero. Closed Loop Configurations A Closed Loop Op Amp circuit uses negative feedback to improve amplifier performance. Negative feedback involves connecting a sample of the output voltage back to the Inverting input of the Op Amp with a resistor network as shown. This feedback voltage is a sample of the output voltage applied 180 out of phase with the input. The amount of feedback is determined by a voltage divider involving R f and R i. The feedback ratio B = R i /(R i + R f ) and represents a value between 0 and 1 (0 and 100%). The feedback voltage V fb is the voltage at the Inverting input and is B x V OUT. 2
V fb The effect of negative feedback is to Reduce and Stabilize the voltage gain of the amplifier. Inverting Amplifier Configuration In the Inverting Amplifier configuration the V IN signal is connected to the Inverting Input. Note that there are differences in the labeling standards for the resistors. Note: the negative sign for the voltage gain indicates that the input and output waveforms for this amplifier are 180 out of phase. The closed loop voltage gain of this amplifier A V,CL = - R f /R IN Examples 1. If R f = 10 kω and R IN = 1 kω, what are the feedback ratio and the closed loop voltage gain for the amplifier. Feedback ratio B = 1 kω/( 1 kω + 10 kω) = 0.091 = 9.1 % The closed loop voltage gain A V,CL = - 10 kω/1 kω = - 10 2. Repeat the calculations for R f = 100 kω and R IN = 2.2 kω Feedback ratio B = 2.2 kω/( 2.2 kω + 100 kω) = 0.02 = 2 % The closed loop voltage gain A V,CL = - 10 kω/1 kω = - 45.5 For these 2 examples when the feedback ratio decreased, the voltage gain increased. 3
Notice that in both these examples that the closed loop voltage has been reduced considerably from the value of 100,000 for the open loop gain and that this gain would be very stable from one amplifier circuit to another because the voltage gain is entirely dependent on the two external resistors and resistors are very stable electronic components. Non-Inverting Amplifier Configuration In the Non-Inverting Amplifier configuration the V IN signal is connected to the Non-Inverting Input. The input and output signals are now in phase. The closed loop voltage gain of this amplifier A V,CL = 1+ R 1 /R 2 Examples 1. If R 1 = 15 kω and R 2 = 1 kω, what are the feedback ratio and the closed loop voltage gain for the amplifier. Feedback ratio B = 1 kω/( 1 kω + 15 kω) = 0.06 = 6 % The closed loop voltage gain A V,CL = 1 + 15 kω/1 kω = 16 2. Repeat the calculations for R f = 120 kω and R IN = 3.3 kω Feedback ratio B = 3.3 kω/( 3.3 kω + 120 kω) = 0.027 = 2.7 % The closed loop voltage gain A V,CL = 1 + 120 kω/3.3 kω = 37.4 Special case of the Non-Inverting Amplifier Non Inverting Voltage Follower Amplifier When the feedback resistor R1 is set to zero a short circuit and the other resistor R2 is removed then the voltage gain of this circuit becomes 1. The input and output signals are in phase. 4
A V,CL = 1+ R 1 /R 2 = 1+ 0/ = 1 Effects of Negative Feedback on R IN and R OUT Negative feedback as has already been seen affects the voltage gain of closed loop amplifiers but it also has effects on R IN and R OUT of Op Amp amplifiers. Non-Inverting Amplifier Negative feedback improves the values for both R IN and R OUT for the Non-Inverting amplifier - makes R IN larger and R OUT smaller. R IN,NonINV = (1 + BA OL )x R IN R OUT,NonInv = R OUT /(1 + BA OL ) Example In a previous example the Feedback ratio B was calculated as 0.06. R IN,NonINV = (1 + 0.06 x 10 5 ) x 2 MΩ = 12 GΩ R OUT,NonInv = 75 Ω/(1 + 0.06 x 10 5 ) = 12.4 mω Inverting Amplifier Negative feedback improves only the value for R OUT for the Non-Inverting amplifier. R IN is small for this configuration. R IN,INV = R 1 R OUT,INV = R OUT /(1 + BA OL ) In a previous example the Feedback ratio B was calculated as 0.091. R IN,INV = 1 kω R OUT,INV = 75 Ω/(1 + 0.091 x 100,000) = 8.2 mω Clearly the Inverting amplifier suffers from a low input resistance. Non Inverting Voltage Follower Amplifier For the voltage follower amplifier R IN = (1 + 1 x 100,000) x 2 MΩ = 200 GΩ R OUT,INV = 75 Ω/(1 + 1 x 100,000) = 0.75 mω An ideal amplifier has an infinite input resistance and a zero output resistance. Clearly the voltage follower is an excellent approximation to an ideal amplifier. 5
Summary Table Parameter Expression Typical value Non-Inverting Amp Voltage gain 1 + R f /R 1 Small to moderate Input Resistance R IN,NonINV = (1 + BA OL )x R IN Very large Output Resistance R OUT,NonInv = R OUT /(1 + BA OL ) Very small Inverting Amp Voltage gain - R f /R 1 Small to moderate Input Resistance R 1 small Output Resistance R OUT,Inv = R OUT /(1 + BA OL ) Very small Voltage Follower Voltage gain 1 small Input Resistance R IN = (1 + A OL )x R IN Extremely large Output Resistance R OUT = R OUT /(1 + A OL ) Extremely small Frequency Response of Op Amp Circuits Open Loop Mode The frequency response of the Open loop circuit is shown. Because of internal resistances and capacitances the Op Amp behaves like a low pass filter with very low corner frequency with a value of 10 Hz. The corner frequency determines the Bandwidth for the circuit. BW = f C 0 = f C. In Open loop mode the Op Amp attenuates input signals above the corner frequency with a roll-off rate of -20 db/decade like a first order low pass filter. 6
Unity Gain Frequency The Unity Gain frequency is the frequency where the voltage gain drops to 1 or 0 db. For a LM 741 Op Amp the Unity Gain frequency is 1 MHz. Closed Loop Frequency Response As we saw earlier the effect of negative feedback is to reduce and stabilize voltage gain. The diagram shows the open loop response as well as another graph for the voltage gain for a closed loop circuit with a closed loop voltage gain called A CL,mid. The voltage gain is significantly less and as a result the corner frequency f c,cl (and the bandwidth) has been increased. This allows us to draw the conclusion that as the closed loop voltage gain is decreased the Bandwidth increases. Gain-Bandwidth Product The conclusion from above can be generalized into a result that states that the Gain-Bandwidth Product = Gain x Bandwidth = Constant value The Gain-Bandwidth product for a LM 741 Op Amp can be determined as Recall that the Gain = 1 at the Unity Gain frequency of 1 MHz Gain-Bandwidth Product = 1 x 1 MHz = 1 MHz 7
Examples What is the gain of a closed loop Op Amp circuit at 50 khz when the Gain-Bandwidth Product is 1 MHz? Gain = 1 MHz/50 khz = 20 What is the Bandwidth of a closed loop Op Amp circuit with a gain of 100 when the Gain-Bandwidth Product is 1 MHz? Bandwidth = 1 MHz/100 = 10 khz Application Note Written by David Lloyd Computer Engineering Program Humber College 8