Basics of impedance matching

Thread Starter

simo_x

Joined Dec 23, 2010
200
Hi all,

I started studying impedance matching and I am facing with a doubt with the basic circuit as shown below:

impedanceMatch.png

In the image, \(\text i X_L\) should be \(-\text i X_L\)
I know that at the frequency of resonance for both components I should have:

\(
\begin{align}
& R_G + \text jX_G + R_L - \text jX_L = R_G + R_L \\
& v_o = {v_i R_L \over R_G + R_L}
\end{align}
\)

Given a frequency of 1 MHz and:
\(
\begin{align}
& R_G = R_L = 50\,\Omega\\
& \omega_0 = 1\,\text{MHz}\\
& Z_L = \text i\omega L = 100\text i \Rightarrow L = 100\,\mu\text{H}\\
& Z_C = -{1 \over \text i\omega C} = -100\text i \Rightarrow C = 10\,\text{nF}
\end{align}
\)

But I tried to put all this stuff into LTspice to see if my result should be OK, but I see that is not.
This is the voltage plot with respect to the frequency..

voltage_freq.png

Of course the bode plot shows a cut off frequency at approximately 100 kHz.
I know there is something wrong, I think I misunderstood some concept..

Could you help me to understand ?
Thank you !
 

Thread Starter

simo_x

Joined Dec 23, 2010
200
Yes, of course : )

Here is the screenshot. I also was visualizing the voltage in the wrong point of the network..

WinXp4.png

: )
 
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