Low Noise Amplifier CG impedance

[jason_class]

Hello All

Kindly see page
http://www.geocities.com/jason_class/circuit_Zs.jpg

I am reading a book on modern communication circuit, then I am stuck at equation 3.56
I do not know how to come up with this equation.
Any kind soul, please teach me step by step in getting this impedance Zs'.
I am not from electronic background but from pure physics back ground.
I am trying to learn but has been stuck here for two weeks. Kindly enlighthen. I must complete this reading as I am lag behind other student in this electronic class.
Kindly enlighthen
Thank you

rgds and thanks
jason

 

[flatulent]

This inductor configuration is called an autotransformer. To better understand the cirucit, draw a wire from the ground on the inductor center tap to the input signal generator. You will see that it is directly across the winding N1. Then there is an output from the winding N2. The voltage stepup is the (N1 + N2)/N1. The impedance stepup is the square of this.

 

[jason_class]

Dear Flatulent

I check some books and saw those inductor type with the winding in side by side.
But this is center tap. How these two types are related?
Kindly enligthen

Thanks a lot

Jason

Added after 9 minutes:

Dear Flatulent

I think I got what you mean.
You mean I should join both the ground for the inductor and also Vi input.
SO I can see the two inductor are actually in parallel?
Am I right


rgds
thanks
Jason

 

[flatulent]

The autotransformer has both windings magnetically coupled and the wires in series. You need to do some library research on 'autotransformer' to better understand this tapped inductor.

**broken link removed** is one tutorial on the web.

 

[jason_class]

Dear Flatulent

I read the tutorial you sent on the link mentioned above.
On page three, the Figure 5 shows a step up transformer right?
So the V2 should be greater than V1 , am I right?
This is true as N2 has more windings.

Then you can find two equation which I do not understand.
1) V1/V2 = N1+N2 /N2

2) V1[ N1+ N2 /N2 ] = V2
Eq(2) will become V2/V1 = N1+ N2 /N2
Then this will contradicts with equation (1), right?


WHich one is right?
Which is the right voltage divider network equation?
Kindly enligthen
If I have make mistakes , pls correct me and I beg your pardon

Thanks


rgds
Jason

 

[jason_class]

Hi Flatulent and all

sorry for my wrong mistake
I believe my eyes have been playing tricks on me
I beg your pardon for the confusion


thanks


rgds
Jason

Added after 3 minutes:

Hi Flatulent

Sorry to have been silly to see the equation wrongly. I have been careless
Thank you so much
I got to understand it now
Really grateful to you for the guidance and help

thank you


rgds Jason