Measurement Based VRM Modeling

Steven M. Sandler PICOTEST

steve@picotest.com

Session 5Power Delivery Networks

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Voltage Regulator Module Unified Model

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1 Model in 1 Second Delivers Large Signal and Small Signal

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Pulse Width Modulated DC-DC Converter – State Time Functions

Continuous Conduction Mode

Discontinuous Conduction Mode

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And Then Integrate and Average the States

𝐼𝑜𝑢𝑡 =𝐼𝑚𝑖𝑛 + 𝐼𝑚𝑎𝑥

2𝐼𝑜𝑢𝑡 =

𝐼𝑚𝑖𝑛 + 𝐼𝑚𝑎𝑥

2

𝐼𝑖𝑛 =𝐼𝑚𝑖𝑛 + 𝐼𝑚𝑎𝑥

2∙ 𝐷𝐼𝑖𝑛 =

𝐼𝑚𝑖𝑛 + 𝐼𝑚𝑎𝑥

2∙ 𝐷

CCMCCM DCMDCM

𝐼𝑖𝑛 =𝐼𝑚𝑎𝑥

2∙ 𝐷𝐼𝑖𝑛 =

𝐼𝑚𝑎𝑥

2∙ 𝐷

𝐼𝑜𝑢𝑡 =𝐼𝑚𝑎𝑥

2∙ 𝐷 + 𝐷2𝐼𝑜𝑢𝑡 =

𝐼𝑚𝑎𝑥

2∙ 𝐷 + 𝐷2

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Complete State Space Average Small Signal Model CCM

VRM

Reverse Transfer

PSRR

Zin Zout

𝑷𝑺𝑹𝑹_𝒅𝑩 = 𝟐𝟎𝒍𝒐𝒈𝑽𝒐 ∙ (𝑹𝒊 ∙ 𝑽𝒐 − 𝟐 ∙ 𝑭𝒔𝒘 ∙ 𝑳𝒐 ∙ 𝑽𝒓𝒂𝒎𝒑

𝑹𝒊 ∙ 𝑽𝒊𝒏𝟐 − 𝟐 ∙ 𝑹𝒊 ∙ 𝑽𝒐 ∙ 𝑽𝒊𝒏 + 𝟐 ∙ 𝑭𝒔𝒘 ∙ 𝑳𝒐 ∙ 𝑽𝒊𝒏 ∙ 𝑽𝒓𝒂𝒎𝒑 + 𝟐 ∙ 𝑨𝒗 ∙ 𝑭𝒔𝒘 ∙ 𝑳𝒐 ∙ 𝑽𝒊𝒏𝑷𝑺𝑹𝑹_𝒅𝑩 = 𝟐𝟎𝒍𝒐𝒈

𝑽𝒐 ∙ (𝑹𝒊 ∙ 𝑽𝒐 − 𝟐 ∙ 𝑭𝒔𝒘 ∙ 𝑳𝒐 ∙ 𝑽𝒓𝒂𝒎𝒑

𝑹𝒊 ∙ 𝑽𝒊𝒏𝟐 − 𝟐 ∙ 𝑹𝒊 ∙ 𝑽𝒐 ∙ 𝑽𝒊𝒏 + 𝟐 ∙ 𝑭𝒔𝒘 ∙ 𝑳𝒐 ∙ 𝑽𝒊𝒏 ∙ 𝑽𝒓𝒂𝒎𝒑 + 𝟐 ∙ 𝑨𝒗 ∙ 𝑭𝒔𝒘 ∙ 𝑳𝒐 ∙ 𝑽𝒊𝒏

𝑹𝒐𝒖𝒕 =

𝟐 ∙ 𝑭𝒔 ∙ 𝑳𝒐 ∙ 𝑹𝒊 ∙ 𝑽𝒊𝒏𝑹𝒊 ∙ 𝑽𝒊𝒏 − 𝟐 ∙ 𝑹𝒊 ∙ 𝑽𝒐 + 𝟐 ∙ 𝑭𝒔𝒘 ∙ 𝑳𝒐 ∙ 𝑽𝒓𝒂𝒎𝒑 +𝑫𝑪𝑹+ 𝑹𝑫𝑺𝒐𝒏

𝟏 + 𝑨𝒗 ∙𝟐 ∙ 𝑭𝒔 ∙ 𝑳𝒐 ∙ 𝑽𝒊𝒏

𝑹𝒊 ∙ 𝑽𝒊𝒏 − 𝟐 ∙ 𝑹𝒊 ∙ 𝑽𝒐 + 𝟐 ∙ 𝑭𝒔𝒘 ∙ 𝑳𝒐 ∙ 𝑽𝒓𝒂𝒎𝒑

𝑹𝒐𝒖𝒕 =

𝟐 ∙ 𝑭𝒔 ∙ 𝑳𝒐 ∙ 𝑹𝒊 ∙ 𝑽𝒊𝒏𝑹𝒊 ∙ 𝑽𝒊𝒏 − 𝟐 ∙ 𝑹𝒊 ∙ 𝑽𝒐 + 𝟐 ∙ 𝑭𝒔𝒘 ∙ 𝑳𝒐 ∙ 𝑽𝒓𝒂𝒎𝒑 +𝑫𝑪𝑹+ 𝑹𝑫𝑺𝒐𝒏

𝟏 + 𝑨𝒗 ∙𝟐 ∙ 𝑭𝒔 ∙ 𝑳𝒐 ∙ 𝑽𝒊𝒏

𝑹𝒊 ∙ 𝑽𝒊𝒏 − 𝟐 ∙ 𝑹𝒊 ∙ 𝑽𝒐 + 𝟐 ∙ 𝑭𝒔𝒘 ∙ 𝑳𝒐 ∙ 𝑽𝒓𝒂𝒎𝒑

𝑹𝒆𝒗𝒆𝒓𝒔𝒆 ≅𝑽𝒐

𝑽𝒊𝒏𝑹𝒆𝒗𝒆𝒓𝒔𝒆 ≅

𝑽𝒐

𝑽𝒊𝒏

𝑹𝒊𝒏 ≅ −𝑽𝒊𝒏𝟐

𝑷𝒊𝒏𝑹𝒊𝒏 ≅ −

𝑽𝒊𝒏𝟐

𝑷𝒊𝒏

Rin and Reverse are insensitive,

so less attention is warranted

Rin and Reverse are insensitive,

so less attention is warranted

𝑳𝒆𝒙𝒄𝒆𝒔𝒔 =𝑳𝒐

𝟏 +𝟐 ∙ 𝑭𝒔 ∙ 𝑳𝒐 ∙ 𝑽𝒊𝒏

𝑹𝒊 ∙ 𝑽𝒊𝒏 − 𝟐 ∙ 𝑹𝒊 ∙ 𝑽𝒐 + 𝟐 ∙ 𝑭𝒔 ∙ 𝑳𝒐 ∙ 𝑽𝒓𝒂𝒎𝒑∙ 𝑨𝒗

+𝑹𝒐

𝟐 ∙ 𝝅 ∙ 𝑮𝑩𝑾𝑳𝒆𝒙𝒄𝒆𝒔𝒔 =

𝑳𝒐

𝟏 +𝟐 ∙ 𝑭𝒔 ∙ 𝑳𝒐 ∙ 𝑽𝒊𝒏

𝑹𝒊 ∙ 𝑽𝒊𝒏 − 𝟐 ∙ 𝑹𝒊 ∙ 𝑽𝒐 + 𝟐 ∙ 𝑭𝒔 ∙ 𝑳𝒐 ∙ 𝑽𝒓𝒂𝒎𝒑∙ 𝑨𝒗

+𝑹𝒐

𝟐 ∙ 𝝅 ∙ 𝑮𝑩𝑾

𝑽𝒐

𝑽𝒄=

𝟐 ∙ 𝑭𝒔 ∙ 𝑳𝒐 ∙ 𝑽𝒊𝒏

𝑹𝒊 ∙ 𝑽𝒊𝒏 − 𝟐 ∙ 𝑹𝒊 ∙ 𝑽𝒐 + 𝟐 ∙ 𝑭𝒔 ∙ 𝑳𝒐 ∙ 𝑽𝒓𝒂𝒎𝒑

𝑽𝒐

𝑽𝒄=

𝟐 ∙ 𝑭𝒔 ∙ 𝑳𝒐 ∙ 𝑽𝒊𝒏

𝑹𝒊 ∙ 𝑽𝒊𝒏 − 𝟐 ∙ 𝑹𝒊 ∙ 𝑽𝒐 + 𝟐 ∙ 𝑭𝒔 ∙ 𝑳𝒐 ∙ 𝑽𝒓𝒂𝒎𝒑

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Measurement Based State-Space Averaged VRM Model

7

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Impedance at the Switching Frequency

8

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Prior Art Ridley Model vs. Unified Sandler Model

9

Control-to-Output Gain Control-to-Output Phase

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Audio SusceptibilityThe inverse of the Power Supply Rejection Ratio

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Large Signal Time Domain and Spectral ContentHarmonic Balance Simulations

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Unified Small and Large Signal VRM Model

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Measured vs ModeledLarge Signal Transient Ripple and Small Signal Gain/Phase

Time Domain Frequency Domain

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Why Do We Need a Measurement Based Model?PCB parasitics can no longer be neglected!

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…and It Works for Multi-Phase DesignsTPS40140 2-Phase Current Mode Controller

Vramp is specified to be 0.5Vpp

And can be adjusted if

necessary to match any of the

other related measurements

Vramp is specified to be 0.5Vpp

And can be adjusted if

necessary to match any of the

other related measurements

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Time Domain Switch Node – Measured vs Modeled

Interestingly the nominal

switching frequency is

specified to be 300kHz and

the EVM measures 261kHz.

More interestingly the EVM

uses a frequency set resistor

of 127kΩ.

While the datasheet states

that the nominal resistance

for 300kHz is 110kΩ.

Interestingly the nominal

switching frequency is

specified to be 300kHz and

the EVM measures 261kHz.

More interestingly the EVM

uses a frequency set resistor

of 127kΩ.

While the datasheet states

that the nominal resistance

for 300kHz is 110kΩ.

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Small Signal AC Output Impedance

VRM Turned Off VRM Turned On

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Does the VRM Data Sheet Work for Your Application?…Good engineering starts with simulation and measurement validation!

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Conclusion

–Demonstration of a measurement based VRM model for small

signal and large signal.

– Fast simulation results for AC, DC, time domain, and spectral

analysis

–Works with DCM and CCM voltage and current mode control

VRMs

–Verified with the well-established Ridley model in simulation for

desired operation

–Measurement validated with commercially available DC-DC

converters

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Thank You,

Ciao