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FEEDBACK INTRODUCTION Most physical systems incorporate some form of feedback. Feedback can be either negative (degenerative) or positive (regenerative). In amplifier design, negative feedback is applied to effect one or more of the following properties: 1. Desensitize the gain; that is, make the value of the gain less sensitive to variations in the value of circuit components. 2. Reduce nonlinear distortion; that is, make the output proportional to the input (make the gain constant). 3. Reduce the effect of noise. 4. Control the input and output impedances. 5. Extend the bandwidth of the amplifier. All of the above desirable properties are obtained at the expense of a reduction in gain. In short, the basic idea of negative feedback is to trade off gain for other desirable properties. The General Feedback Structure Figure. General structure of the feedback amplifier. This is a signal-flow diagram, and the quantities x represent either voltage or current signals. The open-loop amplifier has a gain A; thus its output Xo is related to the input Xi by Xo = A Xi (1) The output Xo is fed to the load as well as to a feedback network, which produces a sample of the output. This sample Xf is related to Xo by the feedback factor B, Xf = Β Xo (2) The feedback signal Xf is subtracted from the source signal Xs to produce the signal Xi , Xi = Xs – Xf (3) So the negative feedback reduces the signal that appears at the input of the basic amplifier. The gain of the feedback amplifier can be obtained by from Eqs. 1-3 : Xo AXi AXi A Af ≡ = = = (4) Xs Xi + Xf Xi + ABXi 1 + AB The quantity Af is called the loop gain. The quantity 1 + AB is called the amount of feedback. In many circuits, the loop gain AB is large, AB » 1, it follows that Af ≈ 1 / B - The gain of the feedback amplifier is almost entirely determined by the feedback network. SOME PROPERTIES OF NEGATIVE FEEDBACK 1.Gain Desensitivity Assume that B is constant. Taking differentials of both sides of Eq. (4) results in dA dAf = (5) (1 + AB )2 Dividing Eq. (5) by Eq. (4) yields dAf 1 dA = Af (1 + AB ) A (6) The amount of feedback, 1 + AB, is also as the desensitivity factor. 2.Bandwidth Extension Consider an amplifier whose high-frequency response is characterized by a single pole. Its gain at mid and high frequencies AM As = (7) 1 + s / ωH where AM denotes the midband gain and ωH is the upper 3-dB frequency. Application of negative feedback, B, results in a closed-loop gain : A( s ) AM / (1 + AM B ) Af ( s) = = 1 + BA( s ) 1 + s / ω H (1 + AM B ) Thus the feedback amplifier will have a midband gain of AM / (1 + AM B ) and an upper 3-dB frequency: ω Hf = ω H (1 + AM B ) Similar a lower 3-dB frequency is ω Lf = ω L / (1 + AM B ) THE FOUR BASIC FEEDBACK TOPOLOGIES Based on the quantity to be amplified (voltage or current) and on the desired form of output (voltage or current), amplifiers can be classified into four categories. Fig. The four basic feedback topologies: (a) voltage-sampling series-mixing (series- shunt) topology; (b) current-sampling shunt-mixing (shunt-series) topology; (c) current-sampling series-mixing (series-series) topology; (d) voltage-sampling shunt- mixing (shunt-shunt) topology. Voltage Amplifiers Since the signal source is a voltage source, it is convenient to represent it in terms of a Thevenin equivalent circuit. In a voltage amplifier the output quantity of interest is the output voltage. It follows that the feedback network should sample the output voltage. Also, because of the Thevenin representation of the source, the feedback signal Xf should be a voltage that can be mixed with the source voltage in series. A suitable feedback topology for the voltage amplifier is the voltage- sampling series-mixing one shown in Fig. (a). This feedback topology is also known as series-shunt feedback, where "series" refers to the input and "shunt" refers to the connection at the output. Current Amplifiers Here the input signal is essentially a current, and thus the signal source is most conveniently represented by its Norton equivalent. The output quantity of interest is current; hence the feedback network should sample the output current. The feedback signal should be in current form so that it may be mixed in shunt with the source current. Thus the feedback topology suitable for a current amplifier is the current-sampling shunt-mixing topology, illustrated in Fig. (b). This feedback topology is also known as shunt-series feedback. Again, the first word in the name (shunt) refers to the connection at the input, and the second word (series) refers to the connection at the output. Transconductance Amplifiers Here the input signal is a voltage and the output signal is a current. It follows that the appropriate feedback topology is the current-sampling series-mixing topology, illustrated in Fig. (c). It is also known as the series-series feedback configuration. Transresistance Amplifiers Here the input signal is current and the output signal is voltage. It follows that the appropriate feedback topology is of the voltage- sampling shunt-mixing type, shown in Fig. (d). It is also known as shunt-shunt feedback. THE SERIES-SHUNT FEEDBACK AMPLIFIER The Ideal Situation The ideal structure of the series-shunt feedback amplifier is shown in Fig. (a). It consists of a open-loop amplifier (the A circuit) and an ideal voltage-sampling series-mixing feedback network (the β circuit). The A circuit has an input resistance Ri a voltage gain A, and an output resistance Ro. Fig. The series-shunt feedback amplifier: (a) ideal structure; (b) equivalent circuit. This circuit of exactly follows the ideal feedback model of and therefore the closed-loop voltage gain Af is given by Vo A Af ≡ = Vs 1 + AB Note that A and B have reciprocal units. This in fact is always the case, resulting in a dimensionless loop gain AB. Input resistance The equivalent circuit model of the series-shunt feedback amplifier is shown in Fig. (b). Here Rif and Rof denote the input and output resistances with feedback. The relationship between Rif and Ri, can be established by considering the circuit in Fig. (a): Vi + BAVi = Ri ⋅ (1 + AB ) Vs Vs Vs Rif ≡ = = Ri = Ri Ii Vi / Ri Vi Vi That is, in this case the negative feedback increases the input resistance by a factor equal to the amount of feedback. The relationship between Rif and Ri, is a function only of the method of mixing and does not depend on the method of sampling. This result is physically intuitive: Since the feedback voltage Vf subtracts from Vs, the voltage that appears across the input becomes quite small. Thus the input current becomes correspondingly small and the resistance becomes large. This relationship can be generalized to the form Z if ( s ) ≡ Z i ( s ) ⋅ (1 + A( s ) B( s ) ) Output resistance To find the output resistance, Rof, of the feedback amplifier in Fig. (a) we reduce Vs to zero and apply a test voltage Vt, at the output, as shown in Fig. Fig. Measuring the output resistance of the feedback amplifier of Fig. (a): Rof = Vt/I. Vt Vt − AVi Rof ≡ and I = I Ro Since Vs=0 , therefore Vi = −Vf = − B ⋅ Vo = − B ⋅ Vt Thus Vt + A ⋅ B ⋅ Vt I= Ro And we can write Ro Rof = 1 + AB That is, the negative feedback in this case reduces the output resistance by a factor equal to the amount of feedback. This relationship does not depend on the method of mixing and depends only on the method of sampling. Finally, we note that this can be generalized to Z of ( s ) ≡ Z o ( s ) / (1 + A( s ) B ( s ) )

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posted: | 8/19/2011 |

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