Library of DC solvers

What is it ?

It is a collection of predefined circuits. One circuit, one solver. Each circuit is fixed, has a set of parameters which values are defined by yourself:

  • power supply voltage
  • tube type,
  • resistor values,
  • bias voltage.

Click an image to access the corresponding solver (if the image is not clickable, then the solver is not yet implemented). Or access them by the main menu.

Though I do not intend to provide – at least for now – a kind of dynamic simulation for each circuit, the plan is to indicate some estimations of the voltage gain, of tube internal resistance, of actual transconductance.

How to use ?

Enter parameters: values of resistors in ohm, kΩ or MΩ, voltages in volt or mV. You cannot type in a decimal separator; instead, use following multipliers: “p” for pico, “n” for nano, “µ” for micro, “m” for milli, “k” for kilo, “M” for mega. For instance: valid values for a 1200Ω resistor are 1200 and 1k2; for a 1.5MΩ, valid entries are 1500000, 1500k and 1M5. You cannot enter anything which value is inferior to 1; rather use a multiplier like “m”. You may enter negative voltages (for the solvers which allow it) like -2 or -100m for respectively minus two volts and minus hundred millivolts.

Power supply values are bound within 50 and 500V.

Once your set of parameters is fine, press button “Solve”. It will yield the result as an image containing:

  • the schematics
  • a bargraph with stacked voltages across anode and cathode resistors and tubes
  • and the operating voltages, currents and dissipated powers.

This JPEG image can be copied or downloaded.

Reliability and accuracy

Operating points are calculated with algorithms based upon the unique and publicly documented Norman Koren’s modeling, which is for sure – like any other model – not perfect specially at low anode voltage or very negative grid voltage. Every time you run a solver, it provides you with a reliability assessment, written in green when:

  • all computed Vgk voltages are negative or null
  • tubes current are the ones expected after NK model
  • stacked voltages (across resistors and tubes) are equal to power supply voltage ±1 or 3 volts
  • count of computing iterations was below upper limit

When any of above conditions is not met, a red comment comes to alert you.

Whenever a grid voltage is reported null, you must question the result; it generally means that the solver did not find a solution where the tube operate in the allowed area of Ia(Vak,Vgk) (see the anode characteristics of the tube) because the surrounding conditions imposed by resistors, supply and bias voltages, or the other triode (in circuits built with 2 tubes) did not allow the tube to operate normally.

Please keep in mind

  • you may rely on DC solutions as long as you enter realistics values for the parameters (supply voltage, resistors) and that tubes operate with a negative Vgk;
  • nevertheless, like with any computed result, you better never trust outputs: check the reality of calculated voltages and currents; the solver may report it did converge, but the resulting figures must be interpreted by you: are 30W power dissipation, 500mA cathode current or 3kV anode-cathode voltage realistic ?

Note: when using a tube which grid and cathode are at high voltages (i.e. cascode, DC coupled cathode follower, etc.), do not forget that you may exceed the cathode-filament max voltage in a practical circuit; the solver is unaware of that and will not issue any warning.

Small signal

A few circuits provide you with an estimation of some small signal parameters, computed for the given operating point, by applying variations to conditions: internal resistance of the tube, transconductance, gain.

Note: the same collection of solvers is available too as a an application for PC running under Windows, see Application for Windows PC

Single triode circuits

Basic gain stage
cathode follower
Self-bias cathodyne
phase inverter
(also cathode follower)
Fixed-bias cathodyne
phase inverter

Dual triode circuits

Gain stage
+DC-coupled cathode follower
Cascode SRPP
Phase inverter
fixed or cathode bias
Phase inverter: constant-current bias