SLUAA12 March   2020 TPS53681

 

  1.   Selection Considerations for Output Capacitors of Multiphase Voltage Regulators Part 1
    1.     Trademarks
    2. 1 Introduction
    3. 2 Current Transfer Function Gii_CL(s) of Load Current to Inductor Current
    4. 3 Output Capacitance Calculation Based on Load Transient
      1. 3.1 Steady-state Output Ripple
      2. 3.2 Load Step Transient Response
        1. 3.2.1 Case 1: Small-signal Transient with Unsaturated Loop
        2. 3.2.2 Case 2: Large-signal Transient with Saturated Loop
        3. 3.2.3 Criteria for Loop Saturation
    5. 4 Analytical Calculations and Experimental Verification
    6. 5 Conclusions
    7. 6 References

4 Analytical Calculations and Experimental Verification

See Table 5 for bench test conditions.

Table 5. Bench Test Conditions

Parameters Value
Input voltage: Vin 12V
Output voltage: Vout 1.8V
Load resistor(as processor leakage): Rload 0.1Ohm
Phase number: N 7
Inductance: L 120nH
Switching frequency: fsw 800kHz
Effective output capacitance: Co 2550µF
Measured cross frequency of loop gain: fc 100kHz
Estimated cross frequency of Gii_CL(s): fci 150kHz
Selected blanking time: tblank 60ns

In Figure 12, both undershoot and overshoot are unsaturated.

waveform-01-load-transient-waveforms-of-example-1-sluaa12.pngFigure 12. Load Transient Waveforms of Example 1

In this situation, load transient is "light" to both upward and downward load step, the response of emulated first-order linear system caused by load step, can be followed very well by real current, unsaturated undershoot and overshoot are symmetrical.

In Figure 13, undershoot is unsaturated while overshoot is saturated.

waveform-02-load-transient-waveforms-of-example-2-sluaa12.pngFigure 13. Load Transient Waveforms of Example 2

In this situation, load transient is still "light" to upward load step, but "heavy" to downward load step, linear system response can be followed upwards, but cannot be followed downwards due to physical limitation, causing overshoot higher than undershoot.

In Figure 14, both undershoot and overshoot are saturated.

waveform-03-load-transient-waveforms-of-example-3-sluaa12.pngFigure 14. Load Transient Waveforms of Example 3

In this situation, load transient is "heavy" to both upward and downward load step, linear system response cannot be followed due to physical limitation, causing both undershoot and overshoot higher. Besides, pay attention to the upward load step in example 3, this is only partial saturated as kmax is relatively high. Isum cannot follow linear system response at the very beginning, but can follow second half of load step. However if you look at downward, it can never follow the linear response caused by falling output current.

By using all of the equations listed in Section 3.2, we can easily get the calculated undershoot and overshoot voltage. Review Table 6 for all results below of calculations and bench test, analytical and experimental results are able to match without much difference.

Table 6. Calculations and Bench Test

Example Number Calculated Undershoot(mV) Bench Undershoot(mV) Calculated Overshoot(mV) Bench Overshoot(mV)
1 33.3 33.6 33.3 33.6
2 62.4 77.1 80.3 84.7
3 198.1 215.7 311.1 322.8