Improvements in the dynamic range and sensitivity of digital MEMS microphones are essential in applications like advanced noise canceling and voice recognition. A cost effective solution to achieve these goals is the companding ADC architecture. Companding ADCs split the dynamic range in several segments with different quantization noise levels, relaxing power constraints. A common problem of companding microphones are audible artifacts generated when the input signal crosses the boundaries between different amplitude segments. We show in this paper a companding ADC architecture that mitigates the boundary artifacts by leveraging the instantaneous and high-resolution time-domain representation of the input signal in a VCO-based ADC. The use of a multi-rate frequency-to-digital converter allows to decouple quantization noise from the VCO frequency, keeping standard audio sampling rates. Co-optimization of the driver and oscillator circuits enables our VCO-ADC to reach \textgreater 112dBc of peak SFDR without a feedback DAC, keeping a Giga-Ohm input impedance compatible with a capacitive MEMS. We show measurements of a 0.13 $μ$m ASIC implementing a complete readout circuit for a digital MEMS microphone. This includes two analog channels and the digital signal processing and calibration blocks required to deliver a standard single-bit PDM output. This ADC reaches a dynamic range of 114.3dB with a power budget under 400 uW, a Schreier FoM_{SNDR} of 171.0 dB and a FoM_{DR} of 191.3 dB.