# The harmonics impact study of a DC-DC buck converter through a power delivery network

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6,136 citations

### "The harmonics impact study of a DC-..." refers background in this paper

...The inductor (LVRM) and capacitor (CVRM) behave combinedly as a low pass filter....

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...2 can be rewritten as: V 3in (H1(jω1)β1 +H2(jω1, jω2)β2 +H3(jω1, jω2, jω3)β3) +V 2in (H1(jω1)β2 +H2(jω1, jω2)β3) + VinH1(jω1)β3 = KPαV 3 in +KPβV 2 in −KP |Vth|Vin, (3) where, α0 = (α11Y0 + α11(Y1 + YA)− α10Y1) Y0 , (4) β1 = αKP (α11 + α11(YA + Y1)sL− α10Y1sL) , (5) β2 = βKP (α11 + α11(Y1 + YA)sL− α10Y1sL) , (6) β3 = α11 (−KP |Vth|+ (Y1 + YA)(1−KP |Vth|sL)) +α10Y1 (KP |Vth|sL− 1) , (7) α11 = α10α2 Y1 − α8YB α7Y1 − Y2 Y1 , α10 = α3 Y2 − α9Y3 Y2 , (8) α9 = Y3 α3 + α8Y2 α3α7 , α8 = α5 α4 − α6Y3 α4α3 , α7 = 1 + α6Y2 α4α3 , (9) α6 = YBY3 Y2 , α5 = Y2Y3 α3 + α3YB Y2 , α4 = α2 − Y 2 2 α3 , (10) α3 = Y2 + Y3, α2 = Y1 + Y2 + YB , (11) α1 = Y1 + YA + Y0, Y1 = 1 RB1 + sLB , YA = 1 sCVRM , (12) Y2 = sCB 1 + sRB2CB , Y0 = 1 ROP + sLVRM , (13) Y3 = ZC +RL ZCRL , ZC = Rpkg2 + sLpkg2 + 1 sCpkg , (14) YB = 1 Rpkg1 + sLpkg , KP = μPCox WP LP , (15) ROP = 1 KP (αVin 2 + βVin − |Vth...

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...The desired output voltage ripples depend on the values of LVRM and CVRM [13]....

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...A feedback connected pulse width modulator (PWM) circuitry is responsible for desired switching frequency (fsw) and constant duty-cycle (D) [13]....

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670 citations

### "The harmonics impact study of a DC-..." refers background or methods in this paper

...The Harmonic Balance (HB) method and Volterra series are the two commonly used methods for distortion analysis of nonlinear systems [7], [8]....

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...Hence, the IIP2h and IIP3h are defined as [7]:...

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...Volterra series defines the mathematical inputoutput relationship for a weakly nonlinear system [7]....

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...Harmonic Distortion quantities The second and the third harmonic distortions (HD2 and HD3) are the ratios of fundamental response (H1(jω1)) with second harmonic response (H2(jω1, jω2)) and third harmonic response (H3(jω1, jω2, jω3)), respectively [7]:...

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...It is one of the reliable solutions for weakly nonlinear systems and easy for manual calculation [7]....

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271 citations

### "The harmonics impact study of a DC-..." refers background in this paper

...A typical PDN is usually comprised of a voltage regulator module (VRM), printed circuit board (PCB), packages and decoupling capacitors [2]....

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200 citations

### "The harmonics impact study of a DC-..." refers background in this paper

...TABLE I PARAMETERS VALUE FOR THE PDN MODEL [14]....

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134 citations

### "The harmonics impact study of a DC-..." refers background in this paper

...Moreover, it is also essential for improvement of quality of the PDN and in harmonic mitigation techniques [5]....

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