Zero-Crossing-Time-Difference Model for Stability Analysis of VCO-Based OTAs

This paper presents the Zero-Crossing-Time-Difference Model (ZCTDM) for a Voltage-Controlled-Oscillator based Operational Transconductance Amplifier (VCO-OTA). The small-signal, linear, discrete-time model provides output current impulses at equidistant time intervals, with their magnitude proportional to the time difference between the zero-crossings of the two VCOs in the VCO-OTA. Compared to the continuous-time phase-domain model (CT-PDM) and the impulse invariant transform model (IITM), ZCTDM accounts for both the high-frequency signal generated at the output near the VCO oscillation frequency and the high-frequency input response. ZCTDM thus captures the complete loop response for a VCO-OTA in a feedback configuration, as long as the output-voltage discharge rate is less than the system update rate, which is the case in most applications. The application of the model is demonstrated with two design examples. The frequency response of the system modeled with ZCTDM is within 0.5dB(RMS) of the response simulated with an extensive behavioral-model, whereas the results derived using CT-PDM and IITM deviate significantly both qualitatively and quantitatively.