PAK Project – Course Outline

Level 1 – How to solve basic diode and transistor circuits (Beta 0v7)
Adobe Acrobat Document 503.9 KB

 Level 1 –How to solve basic diode and transistor circuits  (Link to Level 1 circuit sim download)

PAK101 – Welcome. The Lambert W-function analytical approach

PAK102 – W-function analytical solution for the D+R

PAK103 – Basic BJT analytical solution using the D+R solution

PAK104 – Banwell's CE solution with shunt feedback

PAK105 – Banwell's CE solution with shunt feedback and emitter degeneration

PAK106 – General solution for y·e^y=e^x and y+Ln(y)=x

PAK107 – General solution for y·e^y^2=e^x and y^2+Ln(y)=x

PAK108 – General solution for y^2·e^y=e^x and y +2·Ln(y)=x

PAK109 – General solution for (1/y)e^y=e^x and y–Ln(y)=x

PAK110 – General solution for (1/y^2)e^y=e^x and y–Ln(2y)=x

PAK111 – General solution for y+e^y=e^x and e^y·e^e^y=e^e^x and (x–y)+Ln(x–y)=x

PAK112 – General solution for (1/y)·Ln(y)= x

PAK113 – General solution for (ay^2+by+c)·e^y(1+dy)=e^x and y(1+dy)+Ln(ay^2+by+c)=x

PAK114 – Derivatives dW(e^x)/dx and d^2W(e^x)/dx^2

PAK115 – Indefinite integrals W(x)dx and W(e^x)dx <-NEW

Level 2– How to solve multi-diode circuits (Beta 0v7)
Adobe Acrobat Document 2.0 MB

PAK204 Common Emitter Push-Pull wingspread plots using a spreadsheet. Download

This PDF explains the new W-equation method as used in the wingspread spreadsheet above, and how to run the spreadsheet (ver 0v2)
Adobe Acrobat Document 130.4 KB
Interim PAK209 Early effect equations (0v5b)
Adobe Acrobat Document 183.9 KB


PAK212 VDMOS-Th Electrothermal subcircuit (0v4)
Adobe Acrobat Document 237.5 KB


PAK212 VDMOS-qs Quasisaturation subcircuit (0v1)
Adobe Acrobat Document 305.0 KB


Updated Triode+SIT+jFET subcircuit using the VDMOS (0v9)
Adobe Acrobat Document 917.4 KB

Level 2 – How to solve multi-diode circuits  (Link to Level 2 circuit sim download)

PAK201 – Multi-diode solution for 2D+R

PAK202 – Multi-diode solution for R+[(D+D+R)//(D+R))]

PAK203 – Multi-diode solution for D+(R//(D+R))

PAK204 – Multi-diode solution for (V+D+R)//(-V+D+R) for Vin (Basic PP CE)

PAK205 – Multi-diode solution for (Vb+D)//(-Vb+D)//R for Iin drive and Vin

PAK206 – Multi-diode solution for (Vb+D+R)//(-Vb+D+R)//R for Iin and Vin <-NEW

PAK207 – BJT modelling for Vce saturation

PAK208 – BJT modelling for Beta-fall

PAK209 – BJT modelling for Early effect

PAK210 – BJT modelling for thermal effects

PAK211 – BJT modelling for electro-thermal feedback

PAK212 – MOSFET modelling

PAK213 – Triode Tube modelling

PAK214 – Basic Darlington pair

PAK215 – Basic Complementary Pair (CFP)

PAK216 – Basic Voltage Feedback Pair

PAK217 – Differential pair (BJT LTP)

PAK218 – Basic BJT current mirror & current source

PAK219 – Vbe multiplier

PAK220 – Basic Cascode pair

PAK221 – Rush Pair or Composite Pair

Level 3 – How to solve multi-diode transistor circuits (Beta 0v4a)
Adobe Acrobat Document 1.3 MB

NEW 2020

Alt download:  PAK-Course-304-CFA-analysis-as-CFP.pdf

PAK Course 304 CFA analysis as CFP (0v6)
Adobe Acrobat Document 284.3 KB

 Level 3 – How to solve multi-diode transistor circuits (Link to Level 3 circuit download)

PAK301 – Basic push-pull 

PAK302 – Darlington push-pull

PAK303 – CFP push-pull

PAK304 – Current Feedback Amplifier  <-NEW 2020

PAK305 – Spare

PAK306 – Faran-AB = Idriven Double Displacement Class-AB+C

PAK307 – DoubleCross Double Displacement Class-AB+C Vdriven

PAK307 DoubleCrossTM CE wingspread plots using a spreadsheet Download 

This new idea allows near-zero distortion in the Class-A band of Class-AB up to 3W with certain bias levels. Thermal bias stability is better than standard Class-AB due to near isothermal operation due to a relatively high idle current (~250mA per 2 pair BJT's). Design details and measured distortion is given in Bob Cordell's book 'Designing Audio Power Amplifiers' 2nd Ed. Section 13.8.

LTspice simulation of the basic  DoubleCrossTM CE output stage can be downloaded Level 3 circuit download. It includes the W-solution equations, same as used in the spreadsheet above.

 Level 4 – Solve complete amplifier circuits

PAK401 – Master's level – Wilson Mirrors

PAK402 – Basic Lin “3 stage” topology – general DC solution

PAK403 – Basic Lin topology DC solution as a generalised subcircuit

PAK404 – Lin topology with Beta-fall, Early effect & saturation– DC general solution

PAK405 – Lin topology as a generalised subcircuit (Beta-fall, Early, saturation)

PAK406 – Advantages and disadvantages of current driven output stages

PAK407 – Cube-law amplifier topology – general DC solution

PAK408 – Cube-law amplifier topology as a generalised subcircuit

PAK409 – Current Source Driven topology – general DC solution

PAK410 – Current Source Driven topology as a generalised subcircuit

PAK411 – Faran-AB current driven topology DC solution

PAK412 – Faran-AB current driven topology as a generalised subcircuit

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 Level 5 – Doctorate? –New FFT Analytic Harmonic Analysis, Transient analysis and AC analysis for general Lambert W DC/LF solutions and use in SPICE simulators, automated general Lambert W circuit solution, and transitional Lambert W exact solutions:
PAK501 – New FFT Analytic Harmonic Analysis (AHA) of transistor and tube circuits using the derivatives of general Lambert W DC/LF solutions.
PAK502 – Use of DDE's for amplifier stability analysis (ref Ulsoy). Can jωC and jωL terms be added to DC large signal solutions for steady-state AC analysis?
PAK503 – Add SPICE AC analysis to general DC solutions of transistor and tube circuits.
PAK503 – Software for analytic manipulation of transistor and tube circuit DC solutions.
PAK504 – Exact transitional Lambert W-function solutions for 2nd, 3rd and 4th order polynomials of the form (y^2+by+c) e^y(1+dy) = e^x  for multi-transistor circuit solutions.

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 PAK600 – References, supplementary material

PAK601 – References for PAK course

PAK602 – Spare

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Σ60 Sections. All my work is free for use under Creative Commons 4 Attribution. No liability is accepted. Please let me know if you find any errors. PAK Project is not for profit.


You are welcome to use the “Contact” section to email me.



Ian Hegglun