ELEMENTOS PRINCIPALES
SUSPENSIÓN Suspensión trasera
Phantom zeros [14] are zeros which are realized in the feedback factor [3]. They are thus realized outside the nullor implementation. In the case of a zero
4.6. BANDWIDTH 103
in the relevant part of the asymptotic-gain model is given by:
where is the zero. As can be seen, the zero in the denominator of the asymptotic-gain part cancels with the zero in the numerator of the second fac- tor. The zero is only effectively found in the denominator of the second factor and can therefore be used for the frequency compensation. The characteristic polynomial of a second-order system when one phantom zero is introduced is given by:
As can be seen, the LP product does not change as a result of the phantom zero. Of course, when a phantom zero is practically realized, influences via base resistances, and so on, may also occur. However, the phantom zero is generally near the band edge of a system and therefore the resulting second-order effects will be far beyond the band edge. For an n-th order system, (n-1) phantom zeros are required to alter the sum of the system poles.
A phantom zero is realized when an attenuation in the feedback network is removed beyond a certain frequency. The effectiveness of the phantom zero is determined by the level of the attenuation that is removed. The higher this attenuation is, the more effective this phantom zero is. This can be seen when the unavoidable accompanying pole is examined. Assume that in a reduction of a factor is removed beyond a frequency corresponding to Then the accompanying pole is given by:
This is in the case of a single phantom zero; the reduction is removed by means of a first-order behavior.
An example is given in figure 4.20. Originally, the current from the feedback resistor, was divided between and This resulted in a reduction of With resistor the current path via is made less favorable with respect to the current path via beyond the frequency
The accompanying pole is found at:
104 CHAPTER 4. AMPLIFIERS
4.7
Conclusion
In this chapter the structured design of amplifiers was discussed. It was shown that the three fundamental design aspects: noise, distortion and bandwidth can be treated orthogonally in the design process.
Noise is mainly determined at the input stage and depends on the type of source and input device. Once minimized, the noise performance of the amplifier can no longer improve.
Distortion was divided into clipping distortion and weak distortion. Clipping distortion is mainly found at the output as the signals are the largest there. Weak distortion can be caused by the active devices by means of and distortion, of which distortion is the most severe one. It has been shown that local feedback makes no sense as a measure for reducing distortion. The best way to reduce distortion is by increasing the overall loop gain.
The design of the bandwidth is shown to be governed by the overall loop. Thus bandwidth capability can be improved everywhere in the loop. The LP product is a measure of the maximum attainable bandwidth, i.e. the absolute frequency behavior. This requires the identification of the dominant poles. The dominant poles can be derived from the notion that the sum of the system poles and the sum of the loop poles remains constant when closing the loop. After realizing a sufficient LP product, the poles have to be moved to end up with the required relative frequency behavior, for instance Butterworth.
Four types of frequency compensation methods have been discussed and their influence on the LP product, i.e. the bandwidth capability, was investigated. For the sake of distortion performance, frequency compensation techniques using local feedback are favorable as they use the portion of loop gain, by which the overall loop gain is reduced, for linearizing the stage which is locally fed back. Techniques not using local feedback completely waste this portion.
BIBLIOGRAPHY 105
Bibliography
J.E. Solomon. The monolithic op amp: A tutorial study. IEEE Journal of
Solid-State Circuits, 9(6):314–332, December 1974.
P.R. Gray and R.G. Meyer. MOS operational amplifier design - a tutorial overview. IEEE Journal of Solid-State Circuits, 17(6):969–982, December 1982.
E.H. Nordholt. Design of High-Performance Negative-Feedback Amplifiers. Elsevier, Amsterdam, 1983.
D.R. Frey. Exponential state space filters: A generic current mode de- sign strategy. IEEE Transactions on Circuits and Systems I, 43(l):34–42, January 1996.
Z.Y. Chang and W.M.C. Sansen. Low-Noise Wide-Band Amplifiers in Bipolar and CMOS Technologies. Kluwer Academic Publishers, Dordrecht,
1991.
J. Davidse. Analog Electronic Circuit Design. Prentice Hall International (UK) Ltd, London, 1991.
P.R. Gray and R.G. Meyer. Analysis and Design of Analog Integrated
Circuits. John Wiley & Sons Inc., New York, 1993.
H.T. Friis. Noise figures of radio receivers. Proceedings I.R.E., 32:419–422, 1944.
MicroSim Corporation. Manual Pspice 4.05.
E.M. Cherry and D.E. Hooper. Amplifying Devices and Low-Pass Amplifier
Design. John Wiley and Sons, New York, 1968.
E.M. Cherry. A new result in negative-feedback theory, and its application to audio power amplifiers. IEEE Journal on Circuit Theory and Applica-
tions, 6(3):265–288, July 1978.
S. Rosenstark. Re-examination of frequency response calculations for feed- back amplifiers. International Journal of Electronics, 58(2):271–282, 1985. B.L. Cochrun and A. Grabel. A method for the determination of the trans- fer function of electronic circuits. IEEE Transactions on Circuit Theory, 20(1):16–20, January 1973.
M.S. Ghausi and D.O. Pederson. A new design approach for feedback amplifiers. IRE Transactions on Circuit Theory, 8:274–284, 1961.
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14]
106 AMPLIFIERS
H.W. Bode. Network Analysis and Feedback Amplifier Design. Van Nos- trand, New York, 1945.
C.J.M. Verhoeven, A. van Staveren, and G.L.E. Monna. Structured elec- tronic design, negative-feedback amplifiers. Lecture notes ET4 041, Delft University of Technology, 1999. To appear at John Wiley & Sons LTD, Chichester.
Y.P. Tsividis and P.R. Gray. An integrated NMOS operational ampli- fier with internal compensation. IEEE Journal of Solid-State Circuits,
11(6):748–753, December 1976.
C.A. Makris and C. Toumazou. Current-mode active compensation tech- niques. Electronics Letters, 26(21):1792–1794, October 1990.
R.G.H. Eschauzier, L.P.T. Kerklaan, and J.H. Huijsing. A 100-MHz 100-dB operational amplifier with mulitpath nested miller compensation structure.
IEEE Journal of Solid-State Circuits, 27(12):1709–1716, December 1992.
[15]
[16]
[17]
[18]