Chapter 10: The Operational Amplifiers

Transcription

1 Chapter 10: The Operational Amplifiers Electronic Devices Operational Amplifiers (op-amp) Op-amp is an electronic device that amplify the difference of voltage at its two inputs. It has two input terminals, one of the inputs is called the inverting input (-) and the other is called the non-inverting input. Usually there is a single output. Most op-amps operate with two dc supply voltages, one positive and the other negative, as shown in Figure 1, although some have a single dc supply. Usually these dc voltage terminals are left off the schematic symbol for simplicity but are understood to be there. The Ideal Op-Amp Figure 1:Op-amp symbols. Ideally, op-amps have characteristics (used in circuit analysis): Infinite voltage gain. Infinite input impedance (does not load the driving sources). Zero output impedance (drive any load). Infinite bandwidth (flat magnitude response, zero phase shift). Zero input offset voltage. The ideal op-amp has characteristics that simplify analysis of op-amp circuits. The input voltage, V in, appears between the two input terminals, and the output voltage is A v V in, as indicated by the internal voltage source symbol. The concept of infinite input impedance is particularly a valuable analysis tool for several op-amp configurations. Figure 2: Basic op-amp representations. 77 Assist. Prof. Dr. Hamad Rahman

2 The Practical Op-Amp Practical op-amps have characteristics that often can be treated as ideal for certain situations, but can never actually attain ideal characteristics. In addition to finite gain, bandwidth, and input impedance, they have other limitations. Finite open loop gain. Finite input impedance. Non-zero output impedance. Input current. Input offset voltage. Temperature effects. Characteristics of a practical op-amp are very high voltage gain, very high input impedance, and very low output impedance. Another practical consideration is that there is always noise generated within the op-amp. Noise is an undesired signal that affects the quality of a desired signal. Today, circuit designers are using smaller voltages that require high accuracy, so low-noise components are in greater demand. All circuits generate noise; op-amps are no exception, but the amount can be minimized. Block Diagram Internally, the typical op-amp has a differential input, a voltage amplifier, and a pushpull output. The differential amplifier amplifies the difference in the two inputs. V in + Differential amplifier input stage Voltage amplifier(s) gain stage Push-pull amplifier output stage V out Figure 3: Basic internal arrangement of an op-amp. Input Signal Modes The input signal can be applied to an op-amp in differential-mode or in common-mode. Differential-mode signals are applied either as single-ended (one side on ground) or double-ended (opposite phases on the inputs). Figure 4: Single-ended differential mode. 78 Assist. Prof. Dr. Hamad Rahman

3 Figure 5: Double-ended differential mode. Common-mode signals are applied to both sides with the same phase on both. V in + V out Vin + V out V in Figure 6: Common-mode operation. Usually, common-mode signals are from unwanted sources, and affect both inputs in the same way. The result is that they are essentially cancelled at the output. Common-Mode Rejection Ratio The ability of an amplifier to amplify differential signals and reject common-mode signals is called the common-mode rejection ratio (CMRR), CMRs defined as CCMR = A ol A cm where A ol is the open-loop differential-gain and A cm is the common-mode gain, A cm is zero in ideal op-amp and much less than 1 is practical op-amps. CMRR=100,000 means that desired signal is amplified 100,000 times more than unwanted noise signal. CMRR can also be expressed in decibels as CCMR = 20 log ( A ol A cm ) Example: What is CMRn decibels for a typical 741C op-amp? Solution: The typical open-loop differential gain for the 741C is 200,000 and the typical common-mode gain is 6.3. CCMR = 20 log ( A ol A cm ) = 20 log = 90dB (The minimum specified CMRs 70 db) 79 Assist. Prof. Dr. Hamad Rahman

4 Voltage, Current, and Impedance Parameters V O(p-p) : The maximum output voltage swing is determined by the op-amp and the power supply voltages. V O(p-p) : The maximum output voltage swing is determined by the op-amp and the power supply voltages. I BIAS : The input bias current is the average of the two dc currents required to bias the differential amplifier, I BIAS = I 1 + I 2 2 I OS : The input offset current is the difference between the two dc bias currents, I OS = I 1 I 2 Z IN(d) : The differential input impedance is the total resistance between the inputs Z IN(cm) : The common-mode input impedance is the resistance between each input and ground Z out : The output impedance is the resistance viewed from the output of the circuit Z out Other Parameters Slew rate: The slew rate is the maximum rate of change of the output voltage in response to a step input voltage Slew Rate = V out t Example: Determine the slew rate for the output response to a step input Assist. Prof. Dr. Hamad Rahman

5 Solution: Slew Rate = V out t (+12V) ( 12V) = = 6V/μs 4μ Electronic Devices Negative feedback Negative feedback is the process of returning a portion of the output signal to the input with a phase angle that opposes the input signal. The advantage of negative feedback is that precise values of amplifier gain can be set. In addition, bandwidth and input and output impedances can be controlled. Figure 7 Noninverting Amplifier A noninverting amplifier is a configuration in which the signal is on the noninverting input and a portion of the output is returned to the inverting input. Feedback forces V f to be equal to V in, hence V in is across. With basic algebra, you can show that the closedloop gain of the noninverting amplifier is A cl(ni) = 1 + R f Figure 8: Noninverting amplifier. Example: Determine the gain of the noninverting amplifier shown. Solution: A cl(ni) = 1 + R f = kΩ 3.3kΩ = Assist. Prof. Dr. Hamad Rahman

6 A special case of the noninverting amplifier is when R f =0 and =. This forms a voltage follower or unity gain buffer with a gain of 1. The input impedance of the voltage follower is very high, producing an excellent circuit for isolating one circuit from another, which avoids "loading" effects. Inverting Amplifier An inverting amplifier is a configuration in which the noninverting input is grounded and the signal is applied through a resistor to the inverting input. Figure 9: Inverting amplifier. Feedback forces the inputs to be nearly identical; hence, the inverting input is very close to 0 V. The closed-loop gain of the inverting amplifier is: A cl(i) = R f Example: Determine the gain of the inverting amplifier if R f =82kΩ and =3.3kΩ. Solution: A cl(i) = R f = 82kΩ 3.3kΩ = 24.8 The minus sign indicates inversion Impedances of Noninverting amplifier: Z in(ni) = (1 + A ol B)Z in Generally, assumed to be Z out(ni) = Z out (1 + A ol B) Generally, assumed to be 0 Impedances of Inverting amplifier Z in(i) Z out Z out(i) = (1 + A ol B) Generally, assumed to be Generally, assumed to be 0 Bias Current Compensation For op-amps with a BJT input stage, bias current can create a small output error voltage. To compensate for this, a resistor equal to R f is added to one of the inputs. 82 Assist. Prof. Dr. Hamad Rahman

7 Figure 10: Bias current compensation in the noninverting and inverting amplifier configurations. Bandwidth Limitations Many op-amps have a roll off rate determined by a single low-pass RC circuit, giving a constant -20 db/decade down to unity gain. Op-amps with this characteristic are called compensated op-amps. The sold line represents the open-loop frequency characteristic (Bode plot) for the op-amp. Figure 11: Ideal plot of open-loop voltage gain versus frequency for a typical op-amp. The frequency scale is logarithmic. For op-amps with a -20 db/decade open-loop gain, the closed-loop critical frequency is given by fc(cl)=fc(ol)(1+baol(mid)). Figure 12: Closed-loop gain compared to open-loop gain. 83 Assist. Prof. Dr. Hamad Rahman

8 The closed-loop critical frequency is higher than the open-loop critical frequency by the factor (1+BAol(mid)). This means that you can achieve a higher BW by accepting less gain. For a compensated op-amp, Acl f(cl)=aol fc(ol). The equation, Acl f(cl)=aol fc(ol) shows that the product of the gain and bandwidth are constant. The gain-bandwidth product is also equal to the unity gain frequency. That is ft = Acl fc(cl), where ft is the unity-gain bandwidth. Example: The f T for a 741C op-amp is 1 MHz. What is the BW cl for the amplifier? V in + 741C R f 82 kw V out 3.3 kw A cl(ni) = 1 + R f = kΩ 3.3kΩ = 25.8 BW cl = f T = 1MHz = 38.8 khz A cl Assist. Prof. Dr. Hamad Rahman