 #1
David J
Gold Member
 137
 14
Homework Statement
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I am trying to follow a given example as part of my notes. The example is described below
Using the equation below calculate the insertion loss of the T network of figure 20 (figure 20 is in the attachment) given the values in the table.
I am given a transmission matrix for the T network and values as follows:
##R_S = 300\Omega##
##R_L = 300\Omega##
##R_A = 200\Omega##
##R_B = 200\Omega##
##R_C = 300\Omega##
Homework Equations
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The example equation we are given is as shown below
##A_{IL} = 20\log\left[\frac {AR_L + B +(CR_L + D)R_S)^2 }{R_S +R_L}\right]##
The Attempt at a Solution
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The example solution I am given in my notes is shown below in its entirety :
##A_{IL} = 20\log\left[\frac {AR_L + B +(CR_L + D)R_S)^2 }{R_S +R_L}\right]##
So ##A_{IL} = 20\log\left[\frac{ 1 + \left(\frac{R_A}{R_C}\right)R_L+R_A+R_B+\frac{R_A R_B}{R_C}+\left(\frac{1}{R_C} R_L+\left(1+\frac{R_A}{R_C}\right)\right)R_S}{R_S+R_L}\right]##
So ##A_{IL} = 20\log\left[\frac{ 1 + \left(\frac{200}{300}\right)300+200+200+\frac{200\times200}{300}+\left(\frac{1}{300} 300+\left(1+\frac{200}{300}\right)\right)300}{300+300}\right]##
The example then moves straight to
##A_{IL} = 20\log\left(3.056\right)##
and then an answer of
##A_{IL} = 9.70dB##
The above is what I am given as an example. My problem is that even when I follow each step as shown above I cannot arrive at ##3.056##
I end up with ##3.648055556## which gives an answer of ##11.241dB## which is not correct.
My working out is shown below.
Starting with
##= 20\log\left[\frac{ 1 + \left(\frac{200}{300}\right)300+200+200+\frac{200\times200}{300}+\left(\frac{1}{300} 300+\left(1+\frac{200}{300}\right)\right)300}{300+300}\right]##
##= 20\log\left[\frac{\left(1.666666667\right)\times833.3+\left(1+1.666666667\right)\times300}{600}\right]##
##= 20\log\left[\frac{\left(1.666666667\right)\times833.3+800}{600}\right]##
##= 20\log\left[\frac{2,188.833334}{600}\right]##
##= 20\log\left(3.648055556\right)##
So using my working out I get ##A_{IL} = 11.241dB## which is in correct
As I said in the beginning of this post this is an example question I am given and I am trying to work my way through it. I just need any advice as to why my final result does not match the example. I am obviously doing something wrong somewhere, I just cannot see where. I am thinking its to do with rounding off numbers etc and I am not able to program recurring numbers into my calculator (casio fx100MS) so that may have something to do with it. Maybe I have messed up the calculations out with the brackets or something along those lines. Any advice would, as always be most appreciated.
Thanks
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