EECS 43 Spring 2005 Op Amps EE43 Theory Op Amps 1 Objective The purpose of these experiments is to introduce the most important of all analog building blocks the operational amplifier op amp for short This handout gives an introduction to these amplifiers and a smattering of the various configurations that they can be used in Apart from their most common use as amplifiers both inverting and non inverting they also find applications as buffers load isolators adders subtractors integrators logarithmic amplifiers impedance converters filters low pass high pass band pass band reject or notch and differential amplifiers So let s get set for a fun filled adventure with op amps 2 Introduction Amplifier Circuit Before jumping into op amps let s first go over some amplifier fundamentals An amplifier has an input port and an output port A port consists of two terminals one of which is usually connected to the ground node In a linear amplifier the output signal A input signal where A is the amplification factor or gain Depending on the nature of the input and output signals we can have four types of amplifier gain voltage gain voltage out voltage in current gain current out current in transresistance voltage out current in and transconductance current out voltage in Since most op amps are used as voltage to voltage amplifiers we will limit the discussion here to this type of amplifier The circuit model of an amplifier is shown in Figure 1 center dashed box with an input port and an output port The input port plays a passive role producing no voltage of its own and is modeled by a resistive element Ri called the input resistance The output port is modeled by a dependent voltage source AVi in series with the output resistance Ro where Vi is the potential difference between the input port terminals Figure 1 shows a complete amplifier circuit which consists of an input voltage source Vs in series with the source resistance Rs and an output load resistance RL From this figure it can be seen that we have voltage divider circuits at both the input port and the output port of the amplifier This requires us to re calculate Vi and Vo whenever a different source and or load is used Ri Vs Vi 1 Rs Ri RL Vo Ro R L V V S SO U RCE R i INPUT PORT S 2 R AV i i o OUTPUT PORT R AV i V o A M P L IF IE R Figure 1 Circuit model of an amplifier circuit 1 R LO AD L EECS 43 Spring 2005 Op Amps 3 The Operational Amplifier Ideal Op Amp Model The amplifier model shown in Figure 1 is redrawn in Figure 2 showing the standard op amp notation An op amp is a differential to single ended amplifier i e it amplifies the voltage difference Vp Vn Vi at the input port and produces a voltage Vo at the output port that is referenced to the ground node of the circuit in which the op amp is used ip V p Ri Ro Vi in V p Vi AV i Vo AV i Vo V n V n Figure 2 Standard op amp Figure 3 Ideal op amp The ideal op amp model was derived to simplify circuit analysis and it is commonly used by engineers for first order approximate calculations The ideal model makes three simplifying assumptions Gain is infinite A Input resistance is infinite Ri Output resistance is zero Ro 0 3 4 5 Applying these assumptions to the standard op amp model results in the ideal op amp model shown in Figure 3 Because Ri and the voltage difference Vp Vn Vi at the input port is finite the input currents are zero for an ideal op amp in ip 0 6 Hence there is no loading effect at the input port of an ideal op amp Vi Vs 7 In addition because Ro 0 there is no loading effect at the output port of an ideal op amp Vo A Vi 8 Finally because A and Vo must be finite Vi Vp Vn 0 or Vp Vn 9 2 EECS 43 Spring 2005 Op Amps Note Although Equations 3 5 constitute the ideal op amp assumptions Equations 6 and 9 are used most often in solving op amp circuits I Vp Vn Vn Vout Vin R R1 R1 Vp R2 Vn Vout 2 Vin Vp Vout I Vin Figure 4a Non inverting amplifier Figure 5a Voltage follower Figure 6a Inverting amplifier Vout Vout Vout A 1 A 1 V in Vin Figure 4b Voltage transfer curve of non inverting amplifier Figure 5b Voltage transfer curve of voltage follower Vout A 0 Figure 6b Voltage transfer curve of inverting amplifier Vout Vpower Vout Vpower A 1 Vin Vpower A 1 V in V in V p o w e r Figure 4c Realistic transfer curve of non inverting amplifier V p o w e r Figure 5c Realistic transfer curve of voltage follower A 0 Vin Vpower Figure 6c Realistic transfer curve of inverting amplifier 4 Non Inverting Amplifier An ideal op amp by itself is not a very useful device since any finite non zero input signal would result in infinite output For a real op amp the range of the output signal amplitudes is limited by the positive and negative power supply voltages referred to as the rails However by connecting external components to the ideal op amp we can construct useful amplifier circuits Figure 4a shows a basic op amp circuit the non inverting amplifier The triangular block symbol is used to represent an ideal op amp The input terminal marked with a corresponding to Vp is called the non inverting input the input terminal marked with a corresponding to Vn is called the inverting input 3 EECS 43 Spring 2005 Op Amps To understand how the non inverting amplifier circuit works we need to derive a relationship between the input voltage Vin and the output voltage Vout For an ideal op amp there is no loading effect at the input so Vp Vi 10 Since the current flowing into the inverting input of an ideal op amp is zero the current flowing through R1 is equal to the current flowing through R2 by Kirchhoff s Current Law which states that the algebraic sum of currents flowing into a node is zero to the inverting input node We can therefore apply the voltage divider formula find Vn R1 Vn R1 R2 Vout 11 From Equation 9 we know that Vin Vp Vn so R Vout 1 2 Vin 12 R1 The voltage transfer curve Vout vs Vin for a non inverting amplifier is shown in Figure 4b Notice that the gain Vout Vin is always greater than or equal to one The special op amp circuit configuration shown in Figure 5a has a gain of unity and is called a voltage follower This can be derived from the non inverting amplifier by letting R1 and R2 0 in Equation 12 The voltage transfer curve is shown in Figure 5b A frequently asked question …
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