Advanced Frequency Synthesis by Phase Lock

APPENDIX U

NOISE PRODUCED BY CHARGE PUMP CURRENT UNBALANCE (MISMATCH)

Here, we compute the noise floor produced as a result of mismatch between the two charge pump currents in the presence of ΣΔ modulation (the development is similar to that in Arora et al. [2005]).

If the currents in a charge pump are mismatched, such that one exceeds the other by a small factor k_u, we can look on the process as one where a sequence of positive and negative pulses that causes the ideal quantization noise spectrum is now accompanied by a second mismatch error (u-error) sequence consisting of times the (say) negative pulses in that sequence and − times the positive pulses, as shown in Fig. U.1. Here, the “detected” waveform represents the sample-and-hold value of the phase measured by the PD.^U1 [In a type-2 loop, the whole detected waveform might become slightly higher in order to produce zero average PD output, but we are now not interested in the resulting DC term (assuming it is small enough^U2).] We expect the narrow charge pump pulses to have the same low-frequency content as the sample-and-hold waveform so that the low-frequency noise produced by the mismatch will be the same. This is the same assumption that is made when we represent phase detection as a linear continuous process, as in Fig. ...