Chapter 10: Operational Amplifiers

Chapter 10: Operational Amplifiers

Differential Amplifier Differential amplifier has two identical transistors with two inputs and two outputs. 2

Differential Amplifier Differential amplifier has two identical transistors with two inputs and two outputs. 3

DC Analysis -Differential Amplifier. 4

AC Analysis -Differential Amplifier, this leads to, this leads to, this leads to 5

Use of Current Source 6

Differential Amplifier Operational amplifier or op-amp, is a very high gain differential amplifier with a high input impedance (typically a few meg-ohms) and low output impedance (less than 100 Ω). Note the op-amp has two inputs and one output. 7

Single Ended Input 8

Double-Ended (Differential) Input 9

Single and Double-Ended Output 10

Differential Input and Differenial Output Common Mode Operatin 11

Common Mode Rejection Ratio Differential inputs Common inputs = = + Output Voltage o = + Common Mode Rejection Rate = = ( ) 12

Common Mode Rejection Ratio Example: Calculate the for the circuit measurements shown. 13

Op-Amp Gain Op-Amps have a very high gain. They can be connected open-loop or closed-loop. Open-loop refers to a configuration where there is no feedback from output back to the input. In the open-loop configuration the gain can exceed 10,000. Closed-loop configuration reduces the gain. In order to control the gain of an op-amp it must have feedback. This feedback is a negative feedback. A negative feedback reduces the gain and improves many characteristics of the op-amp. 14

Inverting Op-Amp The signal input is applied to the inverting ( ) input The non-inverting input (+) is grounded The resistor R f is the feedback resistor. It is connected from the output to the negative (inverting) input. This is negative feedback. 15

Gain can be determined from external resistors: R f and R 1 Vo A v = = V i Inverting Op-Amp Gain R R f 1 Unity gain voltage gain is 1 R A f v = R 1 R = R 1 f = 1 The negative sign denotes a 180 phase shift between input and output. Constant Gain R f is a multiple of R 1 16

An understanding of the concept of virtual ground provides a better understanding of how an opamp operates. The non-inverting input pin is at ground. The inverting input pin is also at 0 V for an AC signal. Virtual Ground The op-amp has such high input impedance that even with a high gain there is no current from inverting input pin, therefore there is no voltage from inverting pin to ground all of the current is through R f. 17

Practical Op-Amp Circuits Inverting amplifier Noninverting amplifier Unity follower Summing amplifier Integrator Differentiator 18

Inverting/Noninverting Op-Amps Inverting Amplifier Noninverting Amplifier V o = R R 1 f V 1 V = (1 + o R R f 1 ) V 1 19

Unity Follower V o = V 1 20

Summing Amplifier Because the op-amp has a high input impedance, the multiple inputs are treated as separate inputs. V o R f Rf Rf = V1 + V2 + V3 R1 R 2 R 3 21

Integrator The output is the integral of the input. Integration is the operation of summing the area under a waveform or curve over a period of time. This circuit is useful in lowpass filter circuits and sensor conditioning circuits. 1 (t) = v (t)dt RC vo 1 22

Differentiator The differentiator takes the derivative of the input. This circuit is useful in high-pass filter circuits. dv1(t) vo (t) = RC dt 23

Op-Amp Specifications DC Offset Parameters Even when the input voltage is zero, there can be an output offset. The following can cause this offset: Input offset voltage Input offset current Input offset voltage and input offset current Input bias current 24

Input Offset Voltage (V IO ) The specification sheet for an op-amp indicate an input offset voltage (V IO ). The effect of this input offset voltage on the output can be calculated with V o(offset) = V IO R 1 + R 1 R f 25

Output Offset Voltage Due to Input Offset Current (I IO ) If there is a difference between the dc bias currents for the same applied input, then this also causes an output offset voltage: The input offset Current (I IO ) is specified in the specifications for the op-amp. The effect on the output can be calculated using: V o(offset due to I IO ) = I IO R f 26

Output Offset Voltage Due to Input Offset Current (I IO ) V o(offset due to I IO ) = I IO R f 27

Total Offset Due to V IO and I IO Op-amps may have an output offset voltage due to both factors V IO and I IO. The total output offset voltage will be the sum of the effects of both: Vo (offset) = V o(offset due to VIO ) + V o(offset due to I IO ) 28

Example Calculate the total offset voltage for the given circuit for the op-amp with specified values of input offset voltage = 4 mv and input offset current =150 na. Vo (offset) = V o(offset due to VIO ) + V o(offset due to I IO ) 29

Input Bias Current (I IB ) A parameter that is related to input offset current (I IO ) is called input bias current (I IB ) The separate input bias currents are: I IB = I IB I 2 The total input bias current is the average: IO + IIB = IIB + I 2 IO I IB = I IB + 2 I + IB 30

Frequency Parameters An op-amp is a wide-bandwidth amplifier. The following affect the bandwidth of the op-amp: Gain Slew rate 31

The op-amp s high frequency response is limited by internal circuitry. The plot shown is for an open loop gain (A OL or A VD ). This means that the op-amp is operating at the highest possible gain with no feedback resistor. In the open loop, the op-amp has a narrow bandwidth. The bandwidth widens in closedloop operation, but then the gain is lower. Gain and Bandwidth 32

Slew Rate (SR) Slew rate (SR) is the maximum rate at which an op-amp can change output without distortion. ΔVo SR = (in V/ µ s) Δt The SR rating is given in the specification sheets as V/µs rating. 33

Slew Rate (SR) Example Example: For an op-amp having a slew rate of SR = 2V/μs, what is the maximum closed loop voltage gain that can be used when the input signal varies by 0.5 V in 10 μs. Solution Since o =, o We get = / = = 34

Maximum Signal Frequency The slew rate determines the highest frequency of the op-amp without distortion. f SR 2πV p where V P is the peak voltage 35

Maximum Signal Frequency Example: For the circuit in the figure, determine the maximum frequency that may be used. Op-amp slew rate is SR = 0.5 V/μs Solution For a gain of magnitude,.. rad/s 36

General Op-Amp Specifications Other ratings for op-amp found on specification sheets are: Absolute Ratings Electrical Characteristics Performance 37

Absolute Ratings These are common maximum ratings for the op-amp. 38

Electrical Characteristics Note: These ratings are for specific circuit conditions, and they often include minimum, maximum and typical values. 39

CMRR One rating that is unique to op-amps is CMRR or common-mode rejection ratio. Because the op-amp has two inputs that are opposite in phase (inverting input and the non-inverting input) any signal that is common to both inputs will be cancelled. Op-amp CMRR is a measure of the ability to cancel out common-mode signals. 40

Op-Amp Performance The specification sheets will also include graphs that indicate the performance of the op-amp over a wide range of conditions. 41