Is this formula answer correct?

NomadAU · Jul 21, 2012

Hi,

A bit of an odd question to put on this forum perhaps, but here goes.

I am learning about oscillators, in particular those driven by crystals. I have been reading a very useful article but have come unstuck with one of the formulas provided in the example and wondered if someone might be able to help me...either the article is wrong, or I am calculating it wrong. Here goes...

The formula for calculating the feedback resistor (Rs) is given as
Rs=1/2πƒC2

In the provided example, f=20MHz and C2=27pF, thus
Rs = 1/[(2π)(20MHz)(27pF)]

When I calculate this I get a value of around 294.6 ohms
i.e. 1/((22/7)*2*20000000*0.000000000027) = 294.6127946127946127946

whereas the author gets a value of 398ohms.

Can someone help explain where this difference might be coming from?

john monks · Jul 21, 2012

I get -294.8809i ohms.
Remember this reactance is in the negative direction or what is refered to as "capacitive reactance"

KrisBlueNZ · Jul 21, 2012

I suspect the author did his calculations using different values and when he changed them, he forgot to update his answer, or he accidentally plugged the wrong value into the formula. The 398 ohms answer is correct if C2 is 20 pF.

NomadAU · Jul 26, 2012

Thanks for the confirmation guys...I just wanted to be sure I wasn't screwing up MY calculations somewhere along the way.

Is this formula answer correct?

NomadAU

john monks

KrisBlueNZ Sadly passed away in 2015

NomadAU

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