Resonant circuit question from textbook example

[biker.josh07]

Hello

I am reading RF Circuit Design by Chris Bowick.I am a little mystified by one of the provided examples within the resonant circuit section of the book. The images provide a description of the problem.I am wondering how the effective shunt resistance is calculated to be 4500 Ohms.

First I calculated the resonant radian frequency ? to be (close approximation)

?=1/?(LC)=1/?(0.05x10^(-6)H x 25x10^(-12)F) = 894.4x10^6 rad/s

The series resistance of the inductor is then calculated to be

R(s)=X(s)/Q= ?L/Q = [894.4x10^6 rad/s x 0.05x10^(-6)H]/10
                           = 4.472 Ohms

Then using the formula for calculating the equivalent parallel resistance for a series resistance and reactance.

R(p)=R(s)[1+Q^2]=4.472[1+10^2]=4.472x101=451.7 Ohms

So I am an order of magnitude from the given value in the book.Is there a mistake in the book?If not then please let me know where I went wrong.

Thanks

[jimmc]

Well spotted, your figures are correct and the book is wrong!

I have the fifth printing of the same book (1987) and the 'Q' in this example has been changed to 100 which gives the correct result.

By the way you could have saved a step in your calculation since R(p) = Q* X(Lp) [=Q*X(C)]

Jim

[G0HZU]

I bought my copy of this book about 25 years ago and it's a brilliant book. However, there are other poor design examples besides this simple typo error. Some of the network designs that aim for a specific loaded Q end up with a quite different loaded Q because he uses quite crude or 'rule of thumb' equations in the designs. So the example fails to meet the original loaded Q design requirement by a large margin. eg a design target of QL = 15 ends up with a designed QL of just under 10 if you independently analyse the final network. Quite an error.

But for basic theory on component analysis,  impedance matching and also for basic use of the Smith chart, this book is still one of the best despite its age