Operational Amplifier 1 1 0 Operational Amplifier 1

Operational Amplifier 1

1. 0 Operational Amplifier 1. 1 Introduction 1. 2 Ideal Op-Amp 1. 3 Op-amp input modes 1. 4 Op-amp Parameters 1. 5 Operation • Single-mode • Differential-mode • Common-mode operation • 1. 6 Op-Amps basics • 1. 7 Datasheet • • • 2

1. 1 Introduction Typical IC packages placed on circuit board 3

Uses of Op-Amp n To provide voltage amplitude changes (amplitude and polarity) n Comparators n Oscillators n Filter circuits n Instrumentation circuits 4

Op-Amp Basics Basic Op-amp Note: Terminals for dc supply are omitted 5

Definition • The operational amplifier (op-amp) is a circuit of components integrated into one chip. • Op-amps were used to model the basic mathematical operations: addition, subtraction, integration, differentiation, and etc in electronic analog computers. • A typical op-amp is powered by two dc voltages (+V and –V) and has an inverting (-) and a non-inverting input (+) and an output. 6

n Two dc Supply voltages n n Op-amp schematic symbol +V : Positive -V : Negative n One Output Terminal n Two Input Terminal n n Inverting (-) input Non-inverting (+) input 7

1. 2 Ideal / Practical Op-Amp Ideal Op-Amp • • voltage gain (Av) = ∞ bandwidth = ∞ input impedance (Zin) = ∞ output impedance (Zout) = 0 8

Practical Op-Amp • Voltage gain (Av) very ↑. • Input impedance (Zin) very ↑. • Output impedance (Zout) very ↓. 9

Properties Ideal Op-Amp • • Infinite input impedance Zero output impedance Infinite open-loop gain Infinite bandwidth Zero noise contribution Zero DC output offset Both differential inputs stick together Practical Op-Amp n input impedance 500 k-2 M n output impedance 20 -100 n open-loop gain (20 k to 200 k) n Bandwidth limited (a few k. Hz) n noise contribution n Non-zero DC output offset 10

n Input Impedance (Zin) Input impedance (Zin) is measured across the input terminals. n It is the Thevenin resistance of the internal connection between the two input terminals. n Input impedance (Zin) is the ratio of input voltage (Vin) to input current (Iin). n 11

When Zin = ∞, the input current (Iin) = 0. n So, any current will neither flowing from the source supply into the amplifiers input circuitry, nor will accept current from any external circuit. n In real, the resistance is 500 k to 2 M. n 12

n Output Impedance (Zout) n n n The internal resistance of the op-amp is op-amp output impedance, Zout. n This internal resistance is in series with the load, reducing the output voltage available to the load. The output impedance of the ideal operational amplifier is assumed to be zero acting as a perfect internal voltage source with no internal resistance, so that it can supply as much current as necessary to the load. Real op-amps have output impedance in the range 20 -100 . 13

• Open-Loop Gain (A 0 l) • Open-Loop Gain, Aol is the gain of the op-amp without feedback. • In the ideal op-amp, Aol is infinite. • In real op-amp is (20 k to 200 k). 14

n Bandwidth (BW) n The ideal op-amp will amplify all signals from DC to the highest AC frequencies. n In real op-amps, the bandwidth is rather limited. n n This limitation is specified by the Gain. Bandwidth product, which is equal to the frequency where the amplifier gain becomes unity. Some op-amps, such as 741 family, have very limited bandwidth up to a few k. Hz. 15

n Noise Contribution n In an ideal op amp, all noise voltages produced are external to the op-amp. n Thus any noise in the output signal must have been in the input signal as well. n The ideal op amp contributes nothing extra to the output noise. 16

n Output Offset Voltage n The output offset voltage of any amplifier is the output voltage that exists when it should be zero. n The voltage amplifier sees zero input voltage when both inputs are grounded. This connection should produce a zero output voltage. n If the output is not zero then there is said to be an output voltage present. n In the ideal op amp this offset voltage is zero volts. n In practical op amps the output offset voltage is nonzero. 17

n Both Differential Inputs Stick Together n This means that a voltage applied to one inverting inputs also appears at the other non-inverting inputs. n If we apply a voltage to the inverting input (-) and then connect a voltmeter between the noninverting input (+) and the power supply common, then the voltmeter will read the same potential on non-inverting as on the inverting input. 18

1. 3 Op-Amp Input Modes Single-Ended Differential Mode Input input signal is connected to one input and the other input is grounded. Two possible configuration: 1. Inverting ( ) terminal is grounded and input signal is applied to the non-inverting (+) terminal. In this configuration, the resultant output signal is in phase with the input signal. 19

2. The non-inverting (+) terminal is grounded and input signal is applied to the inverting ( ) terminal. In this configuration, the resultant output signal is in anti-phase with the input signal. 20

Double-Ended Differential Mode Input Ø Two out-of-phase (opposite-polarity) signals are applied to the inputs. Ø The amplified difference between the two inputs appears on the output. 21

Common Mode Input Ø Two signals of same phase, frequency, and amplitude are applied to the inputs which results in Vout = 0 (signals cancel). (Practically, a small output signal will result. ) • This is called common-mode rejection. This type of mode is used to remove unwanted noise signals and do not distort the desired signal. 22

1. 4 Op-Amp Parameters Common-Mode Rejection Ratio (CMRR) – The ability of amplifier to reject the common-mode signals (noise). – Ratio of open-loop gain (Aol) to common-mode gain (Acm): n The higher the CMRR, the better. n open-loop gain (Aol) is high and common-mode gain (Acm) is low. 23

• CMRR = 100, 000 means that the desired input signal (differential) is amplified 100, 000 times more than the unwanted noise (common-mode). • If the amplitudes of the differential input signal and the common-mode noise are equal, the desired signal will appear on the output 100, 000 times greater in amplitude than the noise. • Thus, the noise has been essentially eliminated. 24

Common-Mode Input Voltage – The range of input voltages which, when applied to both inputs, will not cause clipping or other output distortion. Input Offset Voltage (VOS) The differential dc voltage required between the inputs to force the output to zero volts (0 V). n Typical VOS are in the range of 2 m. V or less. n 25

Input Bias Current (IBIAS) – Is the average of the two dc currents required to bias the differential amplifier. – Is the average of both input currents. 26

Input Offset Current (IOS) – The difference in the input bias currents: 27

Offset Voltage error 28

Input Impedance (ZIN) 1. Differential input impedance (ZIN(d)) is the total resistance between the inverting and non-inverting inputs. • Differential impedance is measured by the changes of differential input voltage over changes of bias current: 29

2. Common-mode input impedance (ZIN(cm)) is the resistance between each input and ground. • Common-mode input impedance is measured by the changes of common-mode input voltage over changes of bias current. 30

Output Impedance (Zout) – The resistance viewed from the output terminal of the op-amp. 31

Slew Rate – The maximum rate of change in the output voltage per unit of time. 32

Example 1 The output voltage of a certain op-amp appears as figure below in response to a step input. Determine the slew rate. 33

Negative Feedback In Op-Amp Circuits § Negative feedback is feeding part of the output back to the input to limit the overall gain. § This is used to make the gain more realistic so that the op-amp is not driven into saturation. Remember that regardless of gain, there are limitations of the amount of voltage that an amplifier can produce. § with –ve feedback closed loop gain can be reduced and controlled so that op-amp can function as a linear amplifier. Without negative feedback

Op-Amps With Negative Feedback § The extremely high open-loop gain of an op-amp creates an unstable because a small noise voltage on the input can be amplified to a point where the amplifier is driven out of its linear region. § With negative feedback, the gain can be stabilize and the frequency response can be increased. § Negative feedback takes a portion of the output and applies it back out of phase with the input, creating an effective reduction in gain. § The closed loop gain is much less than the open loop gain and independent of it.

Op-Amps With Negative Feedback Noninverting Amplifier § The closed-loop voltage gain (Acl) is the voltage gain of an opamp with external feedback. § The gain can be controlled by external component values.

Closed-loop Voltage Gain: Noninverting

Op-Amps With Negative Feedback • The voltage-follower amplifier configuration has all of the output signal fed back to the inverting input. • The voltage gain is 1. • This makes it useful as a buffer amp since it has a high input impedance and low output impedance.

Op-Amps With Negative Feedback: Inverting • The inverting amplifier has the output fed back to the inverting input for gain control. • The gain for the inverting op-amp can be determined by the formula below. A cl(I) = - Rf /Ri

Op-Amps With Negative Feedback: Inverting

Effects Of Negative Feedback On Op-Amp Impedances Input Impedance However high the input impedance of an op-amp circuit is, impedance still exists. For a noninverting amplifier it can be determined by the formulas below. B(feedback attenuation) = Ri/(Ri + Rf) Zin(NI) = (1 + Aol. B)Zin Noninverting

Effects Of Negative Feedback On Op-Amp Impedances Output Impedance The output impedance is understood to be low for an op-amp. Its exact value can be determined by the formula below. Z(out)(NI) = Zout/1 + Aol. B Noninverting

Effects Of Negative Feedback On Op-Amp Impedances The input impedance for an inverting amplifier is approximately equal to the input resistor (Ri). Zin(I) Ri The output impedance is very low and in most cases any impedance load can be connected to it with no problem. The exact amount can be determined by the formulas below. B(feedback attenuation) = Ri/Ri + Rf Zout(I) = Zout / (1 + Aol. B) Inverting

Voltage-Follower Impedances: n Voltage-follower is a special case of noninverting amplifier but with B = 1

Effect of an Input Bias Current. Input bias current creates output error voltage (I 1 Rf) in inverting amplifier. Input bias current creates output error voltage in a voltage-follower.

Effect of an Input Bias Current. Input bias current creates output error voltage in noninverting amplifier.

Bias Current Compensation in a Voltage-Follower Input bias current creates an output error voltage that must be compensated for in all of the op-amp configurations. For the voltage-follower this error voltage can be reduced with resistors of the same value in the feedback loop and input.

Bias Current Compensation For the inverting and noninverting configurations this can be accomplished by a resistor in the noninverting part of the circuit that has the same value as the feedback resistor.

Input Offset Voltage Compensation Input offset voltage is small but unavoidable because of internal characteristic differences. The offset null terminals and a potentiometer connected as shown can eliminate this.

Open-Loop Response Remember Op-Amp Gains?

Open-Loop Response The open-loop gain of an op-amp is determined by the internal design and it very high. The high frequency cutoff frequency of an open-loop op-amp is about 10 Hz.

3 d. B Open-Loop Bandwidth • Bandwidth of an ac amplifier is the frequency range between the points where the gain is 3 d. B less than the midrange gain. • In general, it is equal the upper critical frequency (fcu) minus the lower critical frequency (fcl). BW = fcu – fcl • since fcl for op-amp is zero thus, BW = fcu or simply as fc Unity-gain Bandwidth is the frequency at which the gain is equal to one or unity. •

Open-Loop Response The internal RC circuit of an op-amp limits the gain at frequencies higher than the cutoff frequency. The gain of an open-loop op-amp can be determined at any frequency by the formula below. Aol = Aol(mid)/ 1 + f 2/fc 2 Op-amp with internal RC circuit shown externally.

Open-loop response

Open-Loop Response: Phase Shift • As with any RC circuit, phase shift begins to occur at higher frequencies. • An RC lag circuit causes the output signal voltage to lag the input. From previous slide

Complete open-loop frequency response and Phase Response.

Closed-Loop Response Recall for mid range gain of an op-amp. Note: B is the feedback attenuation Op-amps are normally used in a closed-loop configuration with negative feedback. While the gain is reduced the bandwidth is increased. The bandwidth (BW) of a closedloop op-amp can be determined by the formula below. Remember B is the feedback attenuation. BWcl = BWol(1 + BAol(mid))

Closed-Loop Response The gainbandwidth product is always equal to the frequency at which the opamp’s open-loop gain is 0 d. B (unity-gain bandwidth).

Summary Ø The basic op-amp has three terminals: inverting input (-), noninverting (+), and output. Ø An op-amp has a very high open-loop gain, very high input impedance, very lower output impedance, and wide bandwidth. Ø Common-mode occurs when equal in-phase voltages are applied to both terminals, which results in no output. Ø Input offset voltage and current produce an error voltage at the output. These can be compensated for by external components. Ø Gain can be controlled by a resistive feedback loop.

Summary Ø The three op-amp amplifier configurations are inverting, noninverting, and voltage follower. Ø The bandwidth of an op-amp is equal to the upper critical frequency (fcu). Ø The bandwidth increases as the gain is decreased. Ø The internal RC circuits are responsible for high frequency roll-off. Ø The gain-bandwidth product equals the frequency at which unity voltage gain occurs.