This article originally appeared in Linear Audio Volume 2, September 2011. Linear Audio, a book-size printed tech audio resource, is published half-yearly by Jan Didden.
[Part 1 introduces an audio amplifier topology which uses a novel push-pull transimpedance stage that offers a substantial improvement in power supply rejection over standard amplifier configurations. Part 2 discusses the amplifier's biasing, stability and AC performance. Part 3 compares the performance of the new topology with that of a standard amplifier.]
Appendix: Noise in Folded Cascode Stages
The noise contribution of folded cascodes is a major consideration for the newly introduced amplifier topology. In this appendix I will thus present a brief analysis of the major noise sources in folded cascodes. For an exact analysis the mathematical expressions quickly become rather involved. I will hence apply several simplifications; however it is ensured that the result is still valid at least to the extent that it leads to the correct conclusions and design guide lines in typical implementations.
The basic folded cascode consists of three fundamental circuit elements: a common-base transistor, an associated emitter resistor and a voltage reference, which is connected to the base of the cascode transistor. The input of such a stage is in the formof a current, which is applied to the emitter of the common-base transistor. The output is also in the form of a current, available at the collector of the common-base transistor.
In the following we will consider the three fundamental circuit elements to be noise-free (which is denoted by the addition of an asterisk to the according denominator), and model their actual noise contribution by the addition of explicit voltage and current noise sources. In figure A1, Q* embodies the cascode transistor; its voltage and current noise generators are combined and referred to the input by EnQ and InQ. R* forms the emitter resistor, and its noise contribution is represented by the series voltage source EnQ. Finally, the voltage reference is shown as V*, with associated noise generator EnV. The incremental impedance of the voltage reference is of some importance as well, and represented as RV*.
Figure A1: Folded cascode noise generators.
We will now independently analyse every of the four noise generators, and derive their contribution at the output of the folded cascode, i.e. the contributions to the collector current of Q*. The total of these contributions may then be derived by the usual root-mean-square summation, which needs to be applied for uncorrelated sources.
For the analysis we will make the following assumptions: the hFE of Q* is much larger than unity such that base current losses are negligible, the reciprocal of Q* transconductance is much smaller than R*, and hFE • R* is much larger than RV*. All assumptions are valid for typical implementations.
The voltage noise sources of Q* and V* (EnQ and EnV) effectively appear as input signal to an emitter degenerated common-emitter stage. Their contribution at the cascode output is then given by:
Similarly the noise generator EnQ appears in the folded cascode output current as:
The current noise generator of Q* (InQ) has two different contribution paths. First of all, it appears directly in the collector current. That is seen by considering that the sum of the Q* emitter current and InQ is constant (as set by V*, R* and Q* base-emitter voltage); hence InQ must modulate the emitter current of Q*.
As the collector current is equal to the emitter current, the emitter current modulation also appears at the collector of Q*. However, InQ also flows trough the voltage reference. There RV* converts the noise current to a corresponding voltage,which again drives an emitter degenerated common- emitter stage. Note that this mechanism is fully correlated to the first contribution path, and hence the two terms must be linearly added:
Contemplation of (1) trough (4) reveals that, everything else equal, the contribution of any of the four noise generators is reduced by increasing R*. Increasing R* however also increases EnQ (as this transistor is then operated at lower collector current, which increases its voltage noise) and EnQ (higher resistance values imply higher voltage noise); yet this increase is typically proportional to the square root of R* only. Thus overall a net improvement of about √2 (or 3 dB) for doubling R* is gained. InQ reduces itself as well at lower quiescent currents (lower base current implies lower base current noise).
From this discussion it follows that, as a first means to reduce the noise contribution of a folded cascode, the emitter resistor value should be chosen as large as possible. This corresponds to the choice of a low quiescent collector current, and a voltage reference with large DC value. There is usually a lower limit on quiescent current, dictated by distortion concerns. Further noise improvements beyond this point must hence be achieved solely by the increase in reference voltage.