Tip - simplifying resonant freq. calcs. - UK Vintage Radio Repair and Restoration Discussion Forum

Skywave · 3rd Jul 2009, 12:08 pm

Inspired by UK Col's Thread on Simplifying Ohm's Law calculations, here's one I use.

We are all familiar with f=1/2*pi*sq.rt. (LC),

where f = freq. in Hz; L = inductance in Henries; C = capacitance in Farads.

When used in 'our world', you then terms like 10 exp (-6) & 10 exp (-12) all over the place - and the arithmetic gets cumbersome - which can lead to silly answers!

In the standard equation, let L be in uH; C in pF and f in MHz.

Then, f = 1000/6.28*sq.rt.(LC), which is much more manageable.

Al. / Skywave.

AlanBeckett · 3rd Jul 2009, 12:45 pm

Al,
The odd thing is that although I (almost) always use UK Col's methodology for Ohms law, I equally always bash the numbers into my calculator for this application. Mind you, having a calculator with all the right functions on it helps a lot, and I gess I'm less sure of the 'size' of the answer.
Alan

jimmc101 · 3rd Jul 2009, 8:59 pm

If you want a very quick and easy way of calculating resonant circuits then download RFsim99 free from several places eg
http://electroschematics.com/wp-cont.../rf-sim-99.zip
or
http://www.101science.com/RFSim99.exe

(Works on Windows 95 to XP, I don't know about Vista)

Under tools it has a calculator with 4 boxes

Capacitance
Inductance
Impedance
Frequency

Enter any two and it will calculate the other two.

It does much much more including:
Linear simulation from simple schematic input with graphical output
Filter design with the ability to see the effect of 'rounding' component values.

An oldie but goodie

Jim

ukcol · 3rd Jul 2009, 9:18 pm

That looks useful Al.

I can't remember the last time I had a need to calculate resonant frequency, but I do have long term plans to design and build a valve based theremin. With that in mind I have copied your post to a Word document for future use.

BTW it's a pity there is no easy way to type maths text in posts so we don't have to write stuff like "10 exp (-6)" and "f=1/2*pi*sq.rt. (LC)."

Colin M.

ppppenguin · 3rd Jul 2009, 10:00 pm

Quote:

Originally Posted by ukcol

BTW it's a pity there is no easy way to type maths text in posts so we don't have to write stuff like "10 exp (-6)" and "f=1/2*pi*sq.rt. (LC)."

Use FORTRAN or BASIC style computer language.

10^-6 is 10 to the power of -6.

f = 1/ (2*PI*SQRT(L*C))

ukcol · 3rd Jul 2009, 11:02 pm

Sorry Jeffrey, I perhaps didn't make that point very clear.

I had understood what Al. had written in the form that he had had to use. I was trying to say that it was a pity there was no easy way to write mathematical expressions in a post, using standard maths notation as would be found in a maths text book.

Colin M

Skywave · 4th Jul 2009, 10:53 am

If you are using a Windows PC, here are some of the math symbols that are available using the ALT-NUM keypad:

½ Alt 171
¼ Alt 172
α Alt 224
ß Alt 225
π Alt 227
Ω Alt 234
± Alt 241
≈ Alt 247
√ Alt 251
² Alt 253

So, using these, I can write: f = 1/2π√(LC) and: P = V²/R

which is far easier to read than: f = 1/2*pi*SQRT(L*C) and: P = V*V/R

Al. / Skywave.

kalee20 · 4th Jul 2009, 8:32 pm

Don't also forget Alt-230 gives µ.

With resonant frequency calculations, there's another approximation and that is if you make use of π²≈10 (error less than 1%).

Using this, if you know the frequency and the capacitance (or inductance), you can work out the necessary inductance (or capacitance) as follows:

L≈1/40f²C
or
C≈1/40f²L

where C is in µF, L in µH, and f in MHz. This is easy to work out without a calculator!

Skywave · 4th Jul 2009, 10:19 pm

Indeed, Kalee; 4π² ≈ 40: an approximation that I often use.

I can't believe that I left out Alt-230!

Alt-241 ± ; Alt-242 ≥ ; and Alt-243 ≤ are three other useful additions as well.

Incidentally, I, for one, found the equations in your post immediately above so much eaiser to instantly comprehend than the 'traditional PC style'!

Al/ Skywave.

3rd Jul 2009, 12:08 pm	#1
Skywave Rest in Peace Join Date: Jun 2006 Location: Chard, South Somerset, UK. Posts: 7,457	Tip - simplifying resonant freq. calcs. Inspired by UK Col's Thread on Simplifying Ohm's Law calculations, here's one I use. We are all familiar with f=1/2pisq.rt. (LC), where f = freq. in Hz; L = inductance in Henries; C = capacitance in Farads. When used in 'our world', you then terms like 10 exp (-6) & 10 exp (-12) all over the place - and the arithmetic gets cumbersome - which can lead to silly answers! In the standard equation, let L be in uH; C in pF and f in MHz. Then, f = 1000/6.28*sq.rt.(LC), which is much more manageable. Al. / Skywave.

3rd Jul 2009, 12:45 pm	#2
AlanBeckett Rest in Peace Join Date: Dec 2008 Location: Burton upon Trent, East Staffordshire, UK. Posts: 1,686	Re: Tip - simplifying resonant freq. calcs. Al, The odd thing is that although I (almost) always use UK Col's methodology for Ohms law, I equally always bash the numbers into my calculator for this application. Mind you, having a calculator with all the right functions on it helps a lot, and I gess I'm less sure of the 'size' of the answer. Alan

3rd Jul 2009, 8:59 pm	#3
jimmc101 Heptode Join Date: Mar 2009 Location: Portsmouth, Hampshire, UK. Posts: 674	Re: Tip - simplifying resonant freq. calcs. If you want a very quick and easy way of calculating resonant circuits then download RFsim99 free from several places eg http://electroschematics.com/wp-cont.../rf-sim-99.zip or http://www.101science.com/RFSim99.exe (Works on Windows 95 to XP, I don't know about Vista) Under tools it has a calculator with 4 boxes Capacitance Inductance Impedance Frequency Enter any two and it will calculate the other two. It does much much more including: Linear simulation from simple schematic input with graphical output Filter design with the ability to see the effect of 'rounding' component values. An oldie but goodie Jim

3rd Jul 2009, 9:18 pm	#4
ukcol Rest in Peace Join Date: May 2003 Location: Harlaxton, Lincolnshire, UK. Posts: 3,944	Re: Tip - simplifying resonant freq. calcs. That looks useful Al. I can't remember the last time I had a need to calculate resonant frequency, but I do have long term plans to design and build a valve based theremin. With that in mind I have copied your post to a Word document for future use. BTW it's a pity there is no easy way to type maths text in posts so we don't have to write stuff like "10 exp (-6)" and "f=1/2pisq.rt. (LC)." Colin M.

3rd Jul 2009, 11:02 pm	#6
ukcol Rest in Peace Join Date: May 2003 Location: Harlaxton, Lincolnshire, UK. Posts: 3,944	Re: Tip - simplifying resonant freq. calcs. Sorry Jeffrey, I perhaps didn't make that point very clear. I had understood what Al. had written in the form that he had had to use. I was trying to say that it was a pity there was no easy way to write mathematical expressions in a post, using standard maths notation as would be found in a maths text book. Colin M

4th Jul 2009, 10:53 am	#7
Skywave Rest in Peace Join Date: Jun 2006 Location: Chard, South Somerset, UK. Posts: 7,457	Re: Tip - simplifying resonant freq. calcs. If you are using a Windows PC, here are some of the math symbols that are available using the ALT-NUM keypad: ½ Alt 171 ¼ Alt 172 α Alt 224 ß Alt 225 π Alt 227 Ω Alt 234 ± Alt 241 ≈ Alt 247 √ Alt 251 ² Alt 253 So, using these, I can write: f = 1/2π√(LC) and: P = V²/R which is far easier to read than: f = 1/2piSQRT(LC) and: P = VV/R Al. / Skywave.

4th Jul 2009, 8:32 pm	#8
kalee20 Dekatron Join Date: Feb 2007 Location: Lynton, N. Devon, UK. Posts: 7,088	Re: Tip - simplifying resonant freq. calcs. Don't also forget Alt-230 gives µ. With resonant frequency calculations, there's another approximation and that is if you make use of π²≈10 (error less than 1%). Using this, if you know the frequency and the capacitance (or inductance), you can work out the necessary inductance (or capacitance) as follows: L≈1/40f²C or C≈1/40f²L where C is in µF, L in µH, and f in MHz. This is easy to work out without a calculator!

4th Jul 2009, 10:19 pm	#9
Skywave Rest in Peace Join Date: Jun 2006 Location: Chard, South Somerset, UK. Posts: 7,457	Re: Tip - simplifying resonant freq. calcs. Indeed, Kalee; 4π² ≈ 40: an approximation that I often use. I can't believe that I left out Alt-230! Alt-241 ± ; Alt-242 ≥ ; and Alt-243 ≤ are three other useful additions as well. Incidentally, I, for one, found the equations in your post immediately above so much eaiser to instantly comprehend than the 'traditional PC style'! Al/ Skywave.