Different type of load impact on power stage transfer function

Resistive load

The Buck converter test bench in Simplis is as shown in Fig. 1. In Fig. 1 model, we are using resistive load at Buck converter output.

Fig. 1Buck converter model in Simplis with resistive load^[1]

The G_vd simulation from Simplis is as shown in Fig. 2.

Fig. 2Gvd simulation results - resistive load

DC current source as the load

In Fig. 3 model, we are using ideal DC current source at Buck converter output.

Fig. 3Buck converter model in Simplis with DC current source as the load

The G_vd simulation from Simplis is as shown in Fig. 4.

Fig. 4Gvd simulation results - DC current source as the load

Active load with feedback control

Finally, let us use an active load at Buck converter's output. Here the vcvs is to mimic an ideal Opamp. The vccs and the 100MΩ is to mimic an NMOS device.

Fig. 5Buck converter model in Simplis with active load at its output

The G_vd simulation from Simplis is as shown in Fig. 6.

Fig. 6Gvd simulation results - active load

Comparison

Next, we can export the data from Simplis as a csv file and plot the comparison by Matlab as shown in Fig. 7.

Fig. 7Gvd simulation results - comparison

In Ref. [6], the G_vd transfer function is given by:

The complexed pole frequency is given by:

From Eq. 2, the complexed pole frequency is determined by the inductor value L and capacitor value C. Therefore, the type of load at Buck converter output does not impact the complexed pole frequency.

The quality factor Q impact the peaking at complexed pole frequency. The quality factor Q is given by:

From Eq. 3, we can see the loading impedance has a direct impact on the quality factor Q. In the ideal current source and active load case, ideally no matter how the V_OUT changes, the current should stay the same. Therefore, the small signal output impedance is inifinity. As a result, both the ideal current source and active load shows much higher peaking than the resistive load.

Conclusion

The loading impedance does not impact the complexed pole frequency. However, it has a direct impeact on the quality factor Q. Ideal current source and active load shows a higher quality factor Q at the complexed pole frequency.

References and downloads

[1] Fundamentals of power electronics - Chapter 2

[2] Open-loop Buck converter with active load in Simplis - download

[3] Open-loop Buck converter with active load in Simplis - pdf

[4] Open-loop Buck converter with resistive load in Simplis - download

[5] Open-loop Buck converter with DC current source as the load in Simplis - download

[6] Power stage transfer function cheatsheet - Voltage Mode

[6] Power stage transfer function cheatsheet - Voltage Mode (pdf)