(15C) RC, RL and LC circuits

[Johnh]

Here's a trivial but handy little routine to speed up the selection of simple analogue filter circuits using resistance and capacitance (RC), resistance and inductance (RL) and capacitance and inductance (LC). Not going into complex numbers here, this is just for the very simplest calcs.

At a given frequency, it helps answer 6 questions:

1. What is the reactance of a given capacitor? or with the given capacitor, what resistance is needed with it to create a high-pass or low pass filter with the desired corner frequency?

2. as 1, given a reactance, what capacitor is needed

3. and 4, as 1 and 2 but for LR circuits

5, given a capacitance, what inductance is needed to resonate at the specified frequency?

6. or similarly given an inductance, what capacitance is needed?

It's just based on the simple expressions for the magnitude of capacitive reactance: Zc= 1/(2Pi.F.C) and that of inductive reactance Zl = 2Pi.F.L, with resonance being when these expressions are equal.

Only the capacitive reactance Zc is actually coded, just 9 lines on an HP15C, everything else can be found easily by swapping values and use of the 1/x key:

The routine is put on Label C

Input is in Farads, Henrys, Ohms and Hz. Display mode ENG3 or ENG4 is ideal to get clear outputs in uF, nF, pF, mH, kOhms etc


Examples:

A. What is the reactance of a 1nF capacitor at 1000 Hz?

1 EEX CHS 9 Enter
1000
f C

answer: 159.15 e3 = 159k

B. or in reverse, start with the reactance 159k, what is the capacitance?

159000 Enter
1000
f C

answer: 1,001 e-9 = 1nF

To solve similar questions with inductance, press the 1/x key after either entering the reactance, or receiving the answer:

eg

C. What is the reactance of a 10mH inductor at 115 hZ?

0.01 Enter
115
f C
1/x

answer 7.2257 Ohm

D. The inductor above is part of a resonant LC circuit, what should the capacitor be? starting with the above result:

7.2257 (already displayed
RCL 1 (brings back the frequency, or just enter it again)
f C

answer 191.53 e-6 ie, close to 200uF

Code:


001    42 21 13       LBL C
002    44 1       STO 1
003    20       *
004    2       2
005    20       *
006    43 26       PI
007    20       *
008    15       1/x
009    43 32       RTN

Below is a view of it in Pierres HP15C-CE interface after importing it from a VoyagerSave file:

[Steve Simpkin]

A very clever use of a small 9-line program to solve multiple problems! I had a small number of short analog audio design utility programs like this on my HP-11C around 1987. Shortly afterwards I bought a used HP-28C. It only had 2K of RAM but that was more than enough for dozens of small utility programs and equations that were listed on a menu with 4-5 character names. That was a vast improvement over the HP-11C and the HP-28C Solver was also phenomenal. Around 1991 I migrated to a HP-48SX which I used for analog/digital design work for the next 27 years. I still have many of those utility programs loaded on that HP-48SX and in various emulators.

   

[Johnh]

Hi Steve, thanks very much for looking at it.

I often think that in these days where we can easily access extreme analysis power on a desktop, with multiple screens and network backup, the best use of a classic calculator is often to do the simplest tasks very quickly and directly.

[Thomas Klemm]

You might like this article of the old forum:
EE calculations, some not obvious