The other common use is for parallel resistors or "what value do I need to use in parallel with x to give me y?"
But entering the values with their negative exponents and 2nd-key functions can be a little tedious.
Obviously, what I needed was a programmable calculator to store these programs and make it a bit easier.
My old TI-56 is very limited programmatically and is not up to the job.
So I started looking at getting a newer and better programmable calculator. What can I say? I like calculators.
This led me get a nice and inexpensive used TI-84 Plus Silver Edition.
As a bonus, it's a graphing calculator so now I can plot graphs too.
In no time at all I had programs for the three equations mentioned above.
And then I decided to program it to graph the Gain-Frequency response of a valve triode gain stage.
I used the equation in Merlin Blencowe's excellent book "Designing Tube Preamps for Guitar and Bass".
This TI-84 is very easy to program and the manual is quite helpful (unusually for new tech., although this one's not that new).
The program prompts you to enter Rk, Ck, Ra, ra, u.
For the parameters Ra, ra, u, entering 0 will continue with a default value for a ECC83.
The program first gives the approximate half-boost frequency in Hz.
Then it goes on to plot the response on Gain(decibels) v Frequency(Hz) axes.
The program then asks if you want to Save the graph as a "Pic". Enter 0 to not save, or 1/2/3 to save into the calculator's Pic1/Pic2/Pic3.
Program goes back to the graph.
To put a cursor on the plot and read out values, use the "Trace" key.
Y shows Gain in dB.
X shows log(Frequency). To get the Frequency from X, F = InvLog(x) or F = 10^X (see note below)
If the program is run again, the last previously saved graph can be superimposed onto the current graph.
When the graph has finished plotting, press 2nd PRGM[DRAW] > > [to STO] 2[RecallPic] 1/2/3 ENTER
Here's some Photos
TI-84 Plus Silver Edition with frequency plot
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I'm well aware that PCs and smartphones are more powerful for this type of thing, but I'm not the kind of person that's always glued to a smartphone.
I like dedicated tools like this - Instant-On, small and handy for quick use. It was a cheap and easy thing to do.
There are TI emulator apps for smartphones but I haven't tried them.
If there are any other calculator fans out there who would like this program, here it is.
TRIODELG.zip- (651 Bytes) Downloaded 47 times
NOTE - Logarithmic axes
Unfortunately the calculator does not do logarithmic axes, so the frequency x-axis needs an extra bit of calculation.
That's not a problem until you use the Trace function to move a cursor through the graph. The Y/Gain will be shown correctly as the Gain in decibels, but the X/frequency is shown as log(frequency).
If you really need to get the frequency from the cursor readout, you need to perform Inverse-Log(X) or 10^X.
I don't think it's that big a deal as it's unlikely you'll need an exact value. I've included on the graph some frequency markers as a guide.
Looking at the current state-of-the-art HP(Prime) and TI Calculators, it seems that even these do not give you logarithmic axes!! WTF! Sort it out.