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Published byCaitlin Carson Modified over 4 years ago

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**CHAPTER 1: INTRODUCTION TO OPERATIONAL AMPLIFIERS**

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**Objectives Describe basic op-amp characteristics.**

Discuss op-amp modes and parameters. Explain negative feedback. Analyze inverting, non-inverting, voltage follower and inverting op-amp configurations.

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BASIC OP-AMP

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**Symbol and Terminals A standard operational amplifier (op-amp) has;**

Figure 1a: Symbol Figure 1b: Symbol with dc supply connections A standard operational amplifier (op-amp) has; Vout is the output voltage, V+ is the non-inverting input voltage, V- is the inverting input voltage. Typical op-amp operates with 2 dc supply voltages, +ve supply. –ve supply.

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**circuit element designed to perform mathematical **

An op amp is an active circuit element designed to perform mathematical Operations of addition, subtraction, multiplication, division, differentiation, and integration. 741 general purpose op-amp made by Fairchild Semiconductor

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**Internal circuitry of LM741.**

Operational Amplifiers The op amp is built using VLSI techniques. The circuit diagram of an LM 741 from National Semiconductor is shown below. V+ Vin(-) Vo Vin(+) Taken from National Semiconductor data sheet as shown on the web. Internal circuitry of LM741. V-

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**The Ideal Op-Amp The ideal op-amp has; Infinite voltage gain.**

_ + AvVin Zout=0 Zin=∞ Vin Av=∞ Figure 2a: Ideal op-amp representation The ideal op-amp has; Infinite voltage gain. Infinite bandwidth. Infinite input impedance zero output impedance. The input voltage, Vin appears between the two input terminal. The output voltage is AvVin as indicated by the internal voltage source symbol.

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**The Practical Op-Amp Characteristic of a practical op-amp are;**

Very high voltage gain. Very high input impedance. Very low output impedance. Wide bandwidth. _ + AvVin Zout Zin Vin Figure 2b: Practical op-amp representation

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**OP-AMP INPUT MODES AND PARAMETERS**

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**Input Signal Modes A) Single-Ended Input Operation mode;**

One input is grounded. The signal voltage is applied only to the other input. When the signal voltage is applied to the inverting input, an inverted amplified signal voltage appears at the output. (figure 3a) _ + Figure 3a

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**When the signal voltage is applied to the noninverting input with the inverting input grounded,**

a noninverted amplified signal voltage appears at the output. (figure 3b) _ + Figure 3b

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**Two opposite-polarity (out-of-phase) signals are applied to the inputs **

B) Differential Input Operation mode; Two opposite-polarity (out-of-phase) signals are applied to the inputs This type of operation is also referred to as double-ended. The amplified difference between the two inputs appears on the output. _ + Figure 3c

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**This action is called common-mode rejection. **

C) Common-Mode Input Operation mode Two signal voltages of the same phase, frequency and amplitude are applied to the two inputs. (figure 3d) When equal input signals are applied to both inputs, they cancel, resulting in a zero output voltage. This action is called common-mode rejection. Means that this unwanted signal will not appear on the output and distort the desired signal. _ + Figure 3d

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**Common-Mode Rejection Ratio**

Desired signals can appear on only one input or with opposite polarities on both input lines. These desired signals are amplified and appear on the output. Unwanted signals (noise) appearing with the same polarity on both input lines are essentially cancelled by the op-amp and do not appear on the output. The measure of an amplifier’s ability to reject common- mode signal is called CMRR (common-mode rejection ration). Ideally, op-amp provides a very high gain for desired signal (single-ended or differential) zero gain for common-mode signal.

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**The higher the open-loop gain with respect to the common-mode gain,**

the better the performance of the op-amp in terms of rejection of common-mode signals. Therefore; where Aol = open-loop voltage gain Acm = common-mode gain The higher the CMRR, the better. A very high value of CMRR means that the open-loop gain, Aol is high and the common-mode gain, Acm is low. The CMRR expressed in decibels (dB) is

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**Open-Loop Voltage Gain**

Open-loop voltage gain, Aol of an op-amp is the internal voltage gain of the device represents the ration of output voltage to input voltage when there are no external components. The open-loop voltage gain is set entirely by the internal design. Open-loop voltage gain can range up to 200,000 and is not a well-controlled parameter. Data sheet often refer to the open-loop voltage gain as the large-signal voltage gain.

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Example 1 A certain op-amp has an open-loop voltage gain of 100,000 and a common-mode gain of 0.2. Determine the CMRR and express it in decibels. Answer: a) 500,000 b) 114dB

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**Common-Mode Input Voltage Range**

All op-amp have limitation on the range of voltages over which they will operate. The common-mode input voltage range is the range of input voltages which when applied to both inputs will cause clipping or other output distortion. Many op-amp have common-mode input ranges of ±10V with dc supply voltages of ±15V.

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**Input Bias Current The input bias current is**

V2 V1 _ + I2 Vout I1 Figure 4a: Input bias current is the average of the two op-amp input currents. The input bias current is the dc current required by the inputs of the amplifier to properly operate the first stage. By definition, the input bias current is the average of both input currents and is calculated as;

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Input Impedance Two basic ways of specifying the input impedance of an op-amp are Differential. Common-mode. Differential input impedance is the total resistance between the inverting and the noninverting input. Measured by determining the change in bias current for a given change in differential input voltage. ZIN(d) Figure 4b: Differential input impedance

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**Common-mode input impedance is **

the resistance between each input and ground. Measured by determining the change in bias current for a given change in common-mode input voltage. ZIN(cm) Figure 4c: Common-mode impedance

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**Output Impedance The output impedance is**

the resistance viewed from the output terminal of the op-amp as indicated in figure 4d Zout Figure 4d: Op-amp output impedance

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**Slew Rate What is slew rate?**

The maximum rate of change of the output voltage in response to a step input voltage. Is dependent upon the high-frequency response of the amplifier stages within the op-amp. Is measured with an op-amp connected as shown in figure 4e Figure 4e: Test circuit

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**The width of the input pulse must be sufficient **

A pulse is applied to the input, the output voltage is measured as indicated in figure 4f. The width of the input pulse must be sufficient to allow the output to slew from its lower limit to its upper limit. A certain time interval ∆t, is required for the output voltage to go from its lower limit –Vmax to its upper limit +Vmax, once the input step is applied. -Vmax ∆t Vout +Vmax Vin Figure 4f: Step input voltage and the resulting output voltage

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**The slew rate is expressed as**

Where ∆Vout = +Vmax-(-Vmax). The unit is volts per microsecond (V/μs).

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Example 2 The output voltage of a certain op-amp appears as shown in figure below in response to a step input. Determine the slew rate. t 2μs 12μs -9 -10 9 10 Vout(V) Answer: 1.8 V/us

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**OP-AMPS WITH NEGATIVE FEEDBACK**

Negative feedback is a process whereby a portion of the output voltage returned to the input with a phase angle opposed the input signal Advantages: Higher input impedance More stable gain Improved frequency response Lower output impedance More linear operation

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**Closed-Loop Voltage Gain, Acl**

The closed-loop voltage gain is the voltage gain of an op-amp with external feedback. The amplifier configuration consists of the op-amp an external negative feedback circuit that connects the output to the inverting input. The closed-loop voltage gain is determined by the external component values and can be precisely controlled by them.

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**Noninverting Amplifier**

Figure 5: Noninverting amplifier Feedback network Noninverting amplifier is an op-amp connected in a closed-loop with a controlled amount of voltage gain is shown in figure 5. The input signal is applied to the noninverting (+) input. The output is applied back to the inverting (-) input through the feedback circuit (closed loop) formed by the input resistor Ri and the feedback resistor Rf.

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**This creates negative feedback as follows.**

Resistor Ri and Rf form a voltage divider circuit, which reduces Vout and connects the reduced voltage Vf to the inverting input. The feedback voltage is expressed as The closed-loop gain of the noninverting (NI) amplifier is Where Therefore;

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Example 3 Determine the gain of the amplifier in figure below. The open-loop voltage gain of the op-amp is 100,000. 100kΩ 4.7kΩ Answer: 22.3

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Voltage-Follower Figure 6: Op-amp voltage-follower The voltage-follower configuration is a special case of the noninverting amplifier where all the output voltage is fed back to the inverting (-) input by a straight connection. (figure 6) The straight feedback connection has a voltage gain of 1 (no gain). The closed-loop voltage gain of a noninverting amplifier is 1/B.

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**Since B=1, for a voltage-follower,**

the closed-loop voltage gain of the voltage follower is Acl(VF)=1 The most important features of the voltage-follower configuration are very high input impedance very low output impedance. These features make it a nearly ideal buffer amplifier for the interfacing high-impedance sources low-impedance loads.

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**Inverting Amplifier Inverting amplifier**

Aol Figure 7: Inverting Amplifier Inverting amplifier An op-amp connected with a controlled amount of voltage gain. (figure 7) The input signal is applied through a series input resistor Ri to the inverting (-) input. The output is fed back through Rf to the same input. The noninverting (+) input is grounded.

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**For inverting amplifier**

The closed-loop voltage gain is the ratio of the feedback resistance (Rf) to the input resistance (Ri). This gain is independent of the op-amp’s internal open- loop gain. Thus, the negative feedback stabilizes the voltage gain. The negative sign indicates inversion. Therefore;

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Example 4 Given the op-amp configuration in figure below, determine the value of Rf required to produce a closed-loop voltage gain of -100. 2.2kΩ Aol Answer: 220 kΩ

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**Op-amp Impedances Noninverting amplifier: Inverting amplifier:**

Where Zin is the open-loop input impedance (internal) of the op-amp (without feedback connection) Inverting amplifier: Generally, assumed to be Ri Generally, assumed to be 0 Note that the output impedance has the same form for both amplifiers.

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Example 5 Determine the input and output impedances of the amplifier in Figure below. The op-amp datasheet gives Zin = 2MΩ, Zout = 75Ω, and Aol = 200,000. Find the closed-loop voltage gain. Answer: (a) Zin(NI)=17.5GΩ, Zout(NI)=8.6mΩ, (b) Acl(NI) = 23.0

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Example 6 Find the values of the input and output impedances in Figure below. Also, determine the closed-loop voltage gain. The op-amp has the following parameters: Aol = 50,000; Zin = 4MΩ; and Zout = 50 Ω Answer: Zin(I)=1.0kΩ, Zout(I)=980mΩ, Acl(I)=-100

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~End of Chapter 1~

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