Abstract
Chapter 5 presented an introduction to systematic amplifier design, concentrating on noise, bandwidth, and proper signal transfer. It also presented a method to design single-stage negative-feedback amplifiers with low emi susceptibility. This chapter concentrates on designing multiple-stage negative-feedback amplifiers with low specified emi susceptibility. To limit the complexity of the analysis, the number of stages is restricted to two in this work. However, using the method presented in this chapter, a model and equations that can be used for amplifiers with three active stages can also be derived. More than three stages usually leads to stability problems Verhoeven et al. (2003), and therefore is of little interest.
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Notes
- 1.
Note that Mason’s rule (e.g., Gayakwad and Sokoloff 1998) can also be applied to determine \(E_{i1}\), \(E_{i2}\), and \(A_t\).
- 2.
For a bjtoutput stage \(\alpha _2= \xi _2A_2=-\frac{\beta _{ac2}}{1+\beta _{ac2}\frac{j\omega _c}{\omega _{T2}}}\), \(\alpha _{20}= -\beta _{ac}\), and for a fetoutput stage \(\alpha _2= -\frac{\omega _{T2}}{j\omega _c}\), \(\alpha _{20}= -\frac{\omega _{T2}}{j\omega _l}\) are found.
- 3.
It should be noted that some emisusceptibility may remain, even when \(D_2(\omega _c)\) equals zero, since emisusceptibility originates from even-order nonlinearity. Even when the second-order nonlinearity is cancelled, other even-order nonlinearities may not.
- 4.
A comparable discussion holds for fets.
- 5.
Note that \(p_o\) and \(\omega _k\) may not always be separated by a decade or integer numbers of decades.
- 6.
This may also be the case when the amplifier has a differential output stage too. See Appendix D for an accurate model for negative-feedback amplifiers having differential input and differential output stages.
- 7.
- 8.
Datasheets present \(I_{dss}\) and \(U_p\) from which \(\beta _{{\textsc {fet}}}= I_{dss}/U_p^2\) is calculated. It may (just like \(\lambda \)) also be taken from the numerous SPICE models provided by the semiconductor industry.
- 9.
The disturbance can, e.g., now be calculated using the small-signal model of the amplifier with the actual value of its input impedance. This causes differences in the value of \(E_{dist}\) with respect to the ideal case and should be checked. For moderate loop gains of 10–20, \(Z_{in}\) may however be expected to be that large/low that errors in the estimation of \(E_{dist}\) are below 10 \(\%\) as simulations show. These moderate loop gain values are usually easily obtained. Higher loop gains will show less deviation. In case of voltage processing amplifiers \(Z_{in}\) may at frequencies (much) higher than the bandwidth even become lower than \(Z_s\). The effect of this on \(E_{dist}\) should be checked. An iteration between disturbance estimation and amplifier design may be necessary, i.e., orthogonality is lost.
- 10.
or Bessel (\(\zeta = \frac{1}{2}\sqrt{3}\) in case of a second-order behavior, for a maximally flat phase response in the pass band) compensation.
- 11.
Note that the noise performance can be improved by choosing \(R_1//R_2\) to be smaller, e.g., a little smaller than \(R_s\). This increases the load on the output transistor.
- 12.
Simulations must be made with care. The run time should be made large and the time step small. This leads to long simulation times and large data-files. Also, simulation data should be stored when the amplifier is in steady state.
- 13.
With ‘0’ being \(f_c =\) 10 kHz and \(f_l =\) 1 kHz.
- 14.
With \(0.97 \le x \le 1.03\).
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van der Horst, M.J., Serdijn, W.A., Linnenbank, A.C. (2014). Design of emi-Resilient Dual-Stage Amplifiers. In: EMI-Resilient Amplifier Circuits. Analog Circuits and Signal Processing, vol 118. Springer, Cham. https://doi.org/10.1007/978-3-319-00593-5_6
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