Abstract
This chapter provides background information for “image transfer function” related to mismatches in complex filters. The impact of mismatches on the modulator proposed in Chap. 3 is examined, and on the basis of the results, an improved complex ΔΣ modulator is proposed.
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Notes
- 1.
This assumes that the area effects dominate and the edge effects can be ignored.
- 2.
For an integrator with several SC input branches, the thermal noise due to switches referred to input branch C 1a is given by:
$$\frac{{kT}}{{C_{1a} }}\left( {\frac{{2x + 1}}{{x + 1}}} \right)\left( {1 + \frac{{C_{1b} }}{{C_{1a} }} + \frac{{C_{1c} }}{{C_{1a} }} + \cdots } \right),$$However, the opamp input noise referred to the input-branch is given by:
$$\left( {\frac{4}{3}} \right)\frac{{kT}}{{C_{1a} }}\left( {\frac{1}{{x + \frac{{C_{1a} + C_{1b} + \ldots }}{{C_{1a} }}}}} \right)\left(1 + \frac{{C_{1b} }}{{C_{1a} }} + \frac{{C_{1c} }}{{C_{1a} }} + \ldots \right)^2 $$The equation for opamp noise has been derived assuming that all the SC branches have identical time constants. The modified equation reflects the correlated noise injected at the input branches of the integrator.
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Pandita, B. (2011). Architectural-Level Design of the Experimental ΔΣ Modulator. In: Oversampling A/D Converters with Improved Signal Transfer Functions. Analog Circuits and Signal Processing. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0275-6_4
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