The receive path for the sine path can be modeled by Equation 2 through Equation 5.
Equation 2. where
- RXisin: Receiver path sine coil input
- VAMP_LC: LC oscillator signal amplitude
- η: Coupling factor between exciter and receive coil
- fOSC_LC: LC oscillator excitation frequency
- Θ: Instantaneous motor angle
Equation 3. where
- Demodsin: Demodulator sine path output
- VAMP_LC: LC oscillator signal amplitude
- η: Coupling factor between exciter and receive coil
- fOSC_LC: LC oscillator excitation frequency
- Θ: Instantaneous motor angle
- GMIXER: gain due to the mixer
- GBPF: gain due to the bandpass filter
Equation 4. where
- LPFsin: Low pass filter sine path output
- VAMP_LC: LC oscillator signal amplitude
- η: Coupling factor between exciter and receive coil
- Θ: Instantaneous motor angle
- GMIXER: gain due to the mixer
- GBPF: gain due to the bandpass filter
- GLPF: gain due to the lowpass filter
Equation 5. where
- Voutsin: Signal output at the end of sine path
- VAMP_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
- GFIXED is the fixed gain in the signal path, including GLPF and GBPF
- GFIXED = 43.2 for VCC = 5 V
- GFIXED = 28.8 for VCC = 3.3 V
- GMIXER is the gain due to the mixer. The typical value is 0.637.
- GGC 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.