an166

# an166 - INTEGRATED CIRCUITS AN166 Basic feedback theory...

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Philips Semiconductors AN166 Basic feedback theory 1988 Dec INTEGRATED CIRCUITS

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Philips Semiconductors Application note AN166 Basic feedback theory 2 1988 Dec BASIC FEEDBACK THEORY In AN165, the ideal op amp was defined. The ideal parameters are never fully realized but they present a very convenient method for the preliminary analysis of circuitry. So important are these ideal definitions that they are repeated here. The ideal amplifier possesses 1. Infinite gain 2. Infinite input impedance 3. Infinite bandwidth 4. Zero output impedance From these definitions two important theorems are developed. 1. No current flows into or out of the input terminals. 2. When negative feedback is applied, the differential input voltage is reduced to zero. Keeping these rules in mind, the basic concept of feedback can be explored. VOLTAGE-FOLLOWER Perhaps the most often used and simplest circuit is that of a voltage-follower. The circuit of Figure 1 illustrates the simplicity. + E S E OUT E OUT = E S 6 3 2 SL00931 Figure 1. Voltage-Follower Applying the zero differential input theorem, the voltages of Pins 2 and 3 are equal, and since Pins 2 and 6 are tied together, their voltage is equal; hence, E OUT =E IN . Trivial to analyze, the circuit nevertheless does illustrate the power of the zero differential voltage theorem. Because the input impedance is multiplied and the output impedance divided by the loop gain, the voltage-follower is extremely useful for buffering voltage sources and for impedance transformation. The basic configuration in Figure 1 has a gain of 1 with extremely high input impedance. Setting the feedback resistor equal to the source impedance will cancel the effects of bias current if desired. However, for most applications, a direct connection from output to input will suffice. Errors arise from offset voltage, common-mode rejection ratio, and gain. The circuit can be used with any op amp with the required unity gain compensation, if it is required. NON-INVERTING AMPLIFIER Only slightly more complicated is the non-inverting amplifier of Figure 2. The voltage appearing at the inverting input is defined by E 2 + E OUT @ R IN R F ) R IN (1a) Since the differential voltage is zero, E 2 =E S , and the output voltage becomes E OUT + E S ǒ 1 ) R F R IN Ǔ (1b) + E S E OUT 6 3 2 R F R IN R IN || R F E 2 SL00932 Figure 2. Non-Inverting Amplifier It should be noted that as long as the gain of the closed-loop is small compared to open-loop gain, the output will be accurate, but as the closed-loop gain approaches the open-loop value more error will be introduced. The signal source is shown in Figure 2 in series with a resistor equal in size to the parallel combination of R IN and R F . This is desirable because the voltage drops due to bias currents to the inputs are equal and cancel out even over temperature. Thus overall performance is much improved. The amplifier does not phase-invert and possesses high input
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## This note was uploaded on 12/28/2011 for the course ECE 2C taught by Professor Yue during the Fall '08 term at UCSB.

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an166 - INTEGRATED CIRCUITS AN166 Basic feedback theory...

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