The receive path for the sine path can be modeled by Equation 2 through Equation 5.

Equation 2.

where

• RXi_sin: Receiver path sine coil input
• V_{AMP_LC}: LC oscillator signal amplitude
• η: Coupling factor between exciter and receive coil
• f_{OSC_LC}: LC oscillator excitation frequency
• Θ: Instantaneous motor angle

Equation 3.

where

• Demod_sin: Demodulator sine path output
• V_{AMP_LC}: LC oscillator signal amplitude
• η: Coupling factor between exciter and receive coil
• f_{OSC_LC}: LC oscillator excitation frequency
• Θ: Instantaneous motor angle
• G_MIXER: gain due to the mixer
• G_BPF: gain due to the bandpass filter

Equation 4.

where

• LPF_sin: Low pass filter sine path output
• V_{AMP_LC}: LC oscillator signal amplitude
• η: Coupling factor between exciter and receive coil
• Θ: Instantaneous motor angle
• G_MIXER: gain due to the mixer
• G_BPF: gain due to the bandpass filter
• G_LPF: gain due to the lowpass filter

Equation 5.

where

• Vout_sin: Signal output at the end of sine path
• V_{AMP_LC}: LC oscillator signal amplitude
• η: Coupling factor between exciter and receive coil
• Θ: Instantaneous motor angle
• G: Total combined gain of the signal path

The cosine path can be modeled in the same way as sine path.

The total gain of the system is a combination of the gain control, mixer gain, and fixed gain. It can be modeled by Equation 6:

Equation 6.

where

• G_FIXED is the fixed gain in the signal path, including G_LPF and G_BPF
  • G_FIXED = 43.2 for VCC = 5 V
  • G_FIXED = 28.8 for VCC = 3.3 V
• G_MIXER is the gain due to the mixer. The typical value is 0.637.
• G_GC is the variable gain in the signal path. This is either selected by the AGC or the Fixed Gain Control depending on the voltage on the AGC_EN pin.