SLUAA12 March 2020 TPS53681
- Selection Considerations for Output Capacitors of Multiphase Voltage Regulators Part 1
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.
Figure 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.
Figure 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.
Figure 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 |