Pi network impedance matching

[hanhan]

Hi,
Please help me with these questions about pi network impedance matching. I am reading about "IMPEDANCE Matching" but the book only give formula not much explanation. Therefore, I really need your help.
( I also read many online material about pi network but still got stuck.)

 

[MrAl]

Hi,

They seem to be trying to say that the virtual resistor is what the two separated networks see. One sees this as a load the other as a source resistance.

If you remember that the earlier exercises had shown a network that joins a source resistance to a load resistance. In this case the network on the right looks like the load to the network on the left, and the network on the left looks like a source resistance to the network on the right. So they are both satisfied.
However, the drawing of the resistor only makes sense for the network on the left unless we think of the source input voltage being zero for the network on the right.

This should make a lot of sense because we build the network on the left to match the make believe resistor R, and that means we match the source to R perfectly, then we match R to the network on the right so that network matches that R to the output load perfectly. So both networks look like 'R' to each other.

We could analyze this to make sure it is correct of course.


For the Q, isnt that just used to simplify the design procedure? If you show example 4.4 we can take a better look at this too.


The three element network can be formed by adding the two reactances in series into one reactance.

 

[hanhan]

Thank you, MrAl.

They seem to be trying to say that the virtual resistor is what the two separated networks see. One sees this as a load the other as a source resistance.

If you remember that the earlier exercises had shown a network that joins a source resistance to a load resistance. In this case the network on the right looks like the load to the network on the left, and the network on the left looks like a source resistance to the network on the right. So they are both satisfied.
However, the drawing of the resistor only makes sense for the network on the left unless we think of the source input voltage being zero for the network on the right.

This should make a lot of sense because we build the network on the left to match the make believe resistor R, and that means we match the source to R perfectly, then we match R to the network on the right so that network matches that R to the output load perfectly. So both networks look like 'R' to each other.

That makes sense. I have though about it for two day and haven't found the answer.

For the Q, isnt that just used to simplify the design procedure? If you show example 4.4 we can take a better look at this too.

Here is the Example 4.4:

Please see the figure 4.19 in my first post.

 

[hanhan]

Hi,
I have found this material. It may be easier to explain. Please help me with this. Thanks.