SLYT850 February   2024 UCD3138

 

  1.   1
  2. 1Introduction
  3. 2Charge-mode control
  4. 3Control law
  5. 4RHPZ effect and solution
  6. 5Conclusion
  7. 6References

3 Control law

Now that you know how to obtain the electric charge information for each switching cycle, let’s take a look at how to get the sinusoidal input current waveform using the new control law, see Figure 6.

Compared to the traditional control law shown in Figure 2, there are two differences:

  • The current-loop reference is modulated by VIN2, not by VIN.
  • The feedback signal is the electric charge VCHARGE, not ISENSE.
GUID-20240207-SS0I-WVKB-HDGQ-7QM3MP5N4H5J-low.svg Figure 6 Charge-mode control law for PFC.

From Figure 6, the current reference IREF is given by:

Equation 1. I R E F = A     C B

where, IREF is the current-loop reference, A is the voltage-loop output GV, B is Vrms2 used for VIN feedforward control, and C is VIN2.

Looking at Figure 5, Equation 2 expresses the average inductor current in each switching cycle as:

Equation 2. I A V G = ( I 1 + I 2 )     ( T o n + T o f f ) 2     T

where, IAVG is the average inductor current, I1 is the inductor current at the beginning of each switching cycle, I2 is the inductor current peak value in each switching cycle, Ton is the boost switch Q turn on time, Toff is the boost diode D conduction time, and T is the switching period.

Equation 3 calculates the peak voltage of C1 (VCHARGE) in each switching cycle as:

Equation 3. V C H A R G E = I 1   +   I 2     T o f f 2     C

where, C is the capacitance of C1.

In steady state, the control loop forces VCHARGE to equal IREF (see Equation 4):

Equation 4. V C H A R G E = I R E F

For a boost-type converter in steady-state operation, the volt-seconds applied to the boost inductor must be balanced in each switching period (see Equation 5):

Equation 5. T o n     V I N = T o f f     ( V O U T - V I N )

Equation 6 combines Equation 1 through Equation 5:

Equation 6. I A V G = G v     V O U T     C V r m s 2     T     V I N

In Equation 6, since both C and T are constant, and GV, VOUT and Vrms2 do not change in steady state, IAVG follows VIN. When VIN is a sinusoidal waveform, IAVG is also a sinusoidal waveform, thus achieving PFC. Note that Equation 2 and Equation 3 are valid for both CCM and discontinuous conduction mode (DCM); therefore, Equation 6 is valid for both CCM and DCM operation.