For a description of a typical design procedure, see

“Power Supply Design for Vacuum Tube Amplifiers” by Matt Renaud at DIYaudioProjects.com  here 

Reconstructing a classic design chart

Designing the power supply for the BC-221, rekindled an interest in the graph shown above.  It appeared in the ARRL Handbook for many years.  It indicates how the output voltage of an RC filter is a function of the load resistance, R, the transformer series resistance Rs, and filter capacitance, C.  Rather than providing hard and fast values ultimately used in the power supply, it shows important relationships.  For example, series resistance, which is unavoidable and desired anyway for some in-rush current limiting, reduces the available voltage, but also reduces the change in output voltage when the load, R, changes, for example when going from full load to no load.  Targeting operation in the upper right portion of the chart,  a value for  wCR  indicates the order of capacitance, C, that will be needed, given we have chosen a load R (voltage and current) and omega is, for example, 2 pi x (60 Hz).

For years, I wondered where this chart comes from, and how it was constructed.   This led to an interesting journey shown in the following two presentations.

The presentation is broken into two parts.   Part 1, discusses the author of the graph, Otto H. Schade, rectifier waveforms are simulated, and the graph is constructed for the one curve corresponding to Rs = 0 (the uppermost curve).  This restricted case was published as early as 1936 by M.B. Stout.

Part 2 presents the rest of the graph which was laboriously determined by graphical methods for the original paper.  Coming to the rescue is a symbolic solution given by Keng C. Wu in 2010 which permits a numerical solution for the graph.

The online Electronic Design article by Wu is difficult to read due to the small fonts appearing in the equations.  They have been transcribed in the presentation below.