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Entry  Wed Nov 25 20:44:48 2009, kiwamu, Update, Electronics, Multi-resonant EOM --- Q-factor ---- trans.pngeq1.pngimpedance.pngeq2.png
    Reply  Thu Nov 26 02:08:34 2009, Koji, Update, Electronics, Multi-resonant EOM --- Q-factor ---- 
Message ID: 2340     Entry time: Wed Nov 25 20:44:48 2009     Reply to this: 2341
Author: kiwamu 
Type: Update 
Category: Electronics 
Subject: Multi-resonant EOM --- Q-factor ---- 

Now I am studying about the behavior of the Q-factor in the resonant circuit because the Q-factor of the circuit directly determine the performance as the EOM driver.

Here I summarize the fundamental which explains why Q-factor is important.

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The EOM driver circuit can be approximately described as shown in figure below

trans.png

Z represents the impedance of a resonant circuit.

In an ideal case, the transformer just raise the voltage level n-times larger.  Rin is the output impedance of the signal source and usually has 50[Ohm].

The transformer also makes the impedance Z 1/n^2 smaller. Therefore this configuration gives a following relation between Vin and Vout.

eq1.png

 Where G is the gain for the voltage. And G goes to a maximum value when Rin=Z/n2. This relation is shown clearly in the following plot.

 

impedance.png

 Note that I put Rin=50 [Ohm] for calculating the plot.

Under the condition  Rin=Z/n2( generally referred as impedance matching ), the maximum gain can be expressed as;

eq2.png

 

It means that larger Z makes more efficient gain. In our case, interested Z is considered as the impedance at a resonance.

So what we should do is making a resonant circuit which has a higher impedance at the resonance (e.g. high Q-resonant circuit).

 

 

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