OPERATIONAL AMPLIFIERS

BASIC OP-AMP

Symbol and Terminals A standard operational amplifier (op-amp) has; V out 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. Figure 1a: SymbolFigure 1b: Symbol with dc supply connections

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

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

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

OP-AMP INPUT MODES AND PARAMETERS

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

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

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

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

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.

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 A ol = open-loop voltage gain A cm = 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

Open-Loop Voltage Gain Open-loop voltage gain, A ol 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.

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

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.

Input Bias Current 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; Figure 4a: Input bias current is the average of the two op-amp input currents. V2V2 V1V1 _ + I2I2 V out I1I1

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. Z IN(d) Figure 4b: Differential input impedance

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. Z IN(cm) Figure 4c: Common-mode impedance

Output Impedance The output impedance is the resistance viewed from the output terminal of the op-amp as indicated in figure 4d Z out Figure 4d: Op-amp output impedance

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

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 –V max to its upper limit +V max, once the input step is applied. Figure 4f: Step input voltage and the resulting output voltage -V max ∆t V out +V max V in 0

The slew rate is expressed as Where ∆V out = +V max -(-V max ). The unit is volts per microsecond (V/μs).

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 V out (V) Answer: 1.8 V/us

OP-AMPS WITH NEGATIVE FEEDBACK

Closed-Loop Voltage Gain, A cl 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.

Noninverting Amplifier 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 R i and the feedback resistor R f. Figure 5: Noninverting amplifier Feedback network

This creates negative feedback as follows. Resistor R i and R f form a voltage divider circuit, which reduces V out and connects the reduced voltage V f to the inverting input. The feedback voltage is expressed as The closed-loop gain of the noninverting (NI) amplifier is Where Therefore;

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

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. Figure 6: Op-amp voltage-follower

Since B=1, for a voltage-follower, the closed-loop voltage gain of the voltage follower is A cl(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.

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 R i to the inverting (-) input. The output is fed back through R f to the same input. The noninverting (+) input is grounded. A ol Figure 7: Inverting Amplifier

For inverting amplifier The closed-loop voltage gain is the ratio of the feedback resistance (R f ) to the input resistance (R i ). 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;

Example 4 Given the op-amp configuration in figure below, determine the value of R f required to produce a closed-loop voltage gain of A ol 2.2kΩ Answer: 220 kΩ