A study of parallel tuner with voltage‐dependent capacitance

Abstract

SUMMARYA study of varactor tuned LC circuits is presented. Nonlinear time domain circuit differential equation is rewritten in terms of phase plane variables, which can then be solved in closed form. General expressions are derived, which are applicable to any capacitance-voltage relationship. Two types of circuit structures, namely single-ended and balanced, with MOS diodes as the variable capacitance elements, are specifically considered. The nature of the voltage waveforms across the two circuits is determined by phase plane plots. Variation of voltage with time is calculated numerically. It is shown that the voltage waveform for the single-ended circuit is asymmetric, with higher harmonics present. Furthermore, the fundamental resonant frequency is dependent on amplitude of oscillation and could decrease to 94% of its small signal value for large voltage swings. Near 34% control over frequency is calculated, for a bias voltage range of 8 to 1. On the other hand, the balanced structure results in symmetric voltage waveform, with negligible harmonic content. Dependence of frequency on amplitude is weak, only decreasing to 98% of its small signal value, for the largest swings. The tuning range is marginally improved by the balanced structure. The results are compared with those obtained from Fourier-based calculations and experimental data in literature, and good agreement is obtained.

Frequency–amplitude relations for cross‐coupled voltage‐controlled oscillator

“…Considering the largest value for b being equal to unity and u m = 0.95, Equation (16) indicates a downward shift of frequency to 99% of o b . This result is in accordance with numerical calculations of 98% given in [23].…”

“…However, it should be mentioned that the internal transistor capacitance was used for tuning. More details are provided in . As far as variation of frequency with bias is concerned, there are several articles that have reported on tuning ranges of up to 35% .…”

“…The capacitance–voltage relationship for a single MOS varactor diode is given by where C ox is the oxide capacitance and V k is an effective voltage that depends on device parameters. V b is the control bias voltage, and w ( t ) is the time‐dependent voltage across a single variable capacitance diode.…”

“…The total diode voltage is V ( t ) = V b + w ( t ). The aforementioned equation can be rewritten in the following form : where two new quantities C b and β are introduced. C b is the small signal capacitance at the control voltage, and factor β is related to DC control voltage.…”

Parametric CMOS upconverters and downconverters

“…As noted therein, these characteristics are for varactors in a 130-nm CMOS technology. Another viable varactor option is the inversion-mode MOS varactor (IMOSV) [14,15] whose cross section is shown in Figure 11. As illustrated there, the device is a modern MOS transistor with extensive engineering of the source/drain regions both of which are shorted to one another (i.e.…”