Power stage transfer function cheatsheet

Ming Sun

Ming Sun / December 01, 2022

4 min read • ––– views

Buck converter

  • Gvd
`G_{vd} = ubrace(V_g)_(G_{vd0}) * obrace(1)^(1+s//omega_z)/{1+ubrace(s*L/R)_(s//omega_0Q) + ubrace(LC*s^2)_((s//omega_0)^2)} = G_(0)*(1+s/omega_z)/(1+s/(omega_0Q)+(s/omega_0)^2)`
(1)
  • Gid
`G_{id} = V_g/R * (1+sRC)/(1+s*L/R + LC*s^2) = G_(0)*(1+s/omega_z)/(1+s/(omega_0Q)+(s/omega_0)^2)`
(2)
  • Gvg
`G_{vg} = D * 1/{1+s*L/R + LC*s^2} = G_(0)*(1+s/omega_z)/(1+s/(omega_0Q)+(s/omega_0)^2)`
(3)
  • Gig
`G_{ig} = D/R * (1+sRC)/(1+s*L/R + LC*s^2) = G_(0)*(1+s/omega_z)/(1+s/(omega_0Q)+(s/omega_0)^2)`
(4)

Boost converter

  • Gvd
`G_{vd} = V/D^' * (1-s*L/(RD^('2)))/{1+s*L/(RD^('2)) + (LC)/D^('2)*s^2} = G_(0)*(1+s/omega_z)/(1+s/(omega_0Q)+(s/omega_0)^2)`
(5)
  • Gid
`G_{id} = V/(RD^('2)) * (2+sRC)/(1+s*L/(RD^('2)) + s^2*(LC)/(D^('2))) = G_(0)*(1+s/omega_z)/(1+s/(omega_0Q)+(s/omega_0)^2)`
(6)
  • Gvg
`G_{vg} = 1/D^' * 1/{1+s*L/(RD^('2)) + (LC)/D^('2)*s^2} = G_(0)*(1+s/omega_z)/(1+s/(omega_0Q)+(s/omega_0)^2)`
(7)
  • Gig
`G_{ig} = 1/(RD^('2))*(1+sRC)/(1+s*L/(RD^('2)) + s^2*(LC)/(D^('2))) = G_(0)*(1+s/omega_z)/(1+s/(omega_0Q)+(s/omega_0)^2)`
(8)

IBB (inverted Buck-Boost) converter

  • Gvd
`G_{vd} = V/(DD^')*(1-s*(DL)/(RD^('2)))/(1 + s*L/(RD^('2)) + s^2*(LC)/D^('2)) = G_(0)*(1+s/omega_z)/(1+s/(omega_0Q)+(s/omega_0)^2)`
(9)
  • Gid
`G_{id} = -V/(RDD^('2))*(1+D+sRC)/(1+s*L/(RD^('2))+s^2*(LC)/D^('2)) = G_(0)*(1+s/omega_z)/(1+s/(omega_0Q)+(s/omega_0)^2)`
(10)
  • Gvg
`G_{vg} = -D/D^'*1/(1+s*L/(RD^('2))+s^2*(LC)/(D^('2))) = G_(0)*(1+s/omega_z)/(1+s/(omega_0Q)+(s/omega_0)^2)`
(11)
  • Gig
`G_{ig} = D/(RD^('2))*(1+sRC)/(1+s*L/(RD^('2)) + s^2*(LC)/D^('2)) = G_(0)*(1+s/omega_z)/(1+s/(omega_0Q)+(s/omega_0)^2)`
(12)

Summary

We can write the Gvd, Gid, Gvg and Gig in a general form as shown in Eq. 13.

`G = G_(0)*(1+s/omega_z)/(1+s/(omega_0Q)+(s/omega_0)^2)`
(13)
  • The Buck converter transfer function is as shown in Fig. 1.
Buck converter transfer function
Fig. 1Buck converter transfer function
  • The Boost converter transfer function is as shown in Fig. 2.
Boost converter transfer function
Fig. 2Boost converter transfer function
  • The IBB converter transfer function is as shown in Fig. 3.
IBB converter transfer function
Fig. 3IBB converter transfer function

References and downloads

[1] Fundamentals of power electronics - Chapter 2

[2] Power stage transfer function cheatsheet - pdf

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