Recent content by ChasW.

Thank you for your response. True enough, but for the values and topologies I provided, a match for each case is possible. In the general sense, yes. I did select two cases for a single topology, normal L-section, with values that are matchable given both cases. It is a normal L-section because...

Homework Statement I am calculating matching impedances for a source and its load using 2 different L-network topologies. One is: source-parallel-to-C, load-series-to-L and the other is: source-parallel-to-L, load-series-to-C. I go through all the calculations and notice that...

I think this helped. Starting from R_T+jX_T=R_A(1+jB_CR_T-B_CX_T)+(X_A+X_L)(-j+B_CR_T+jB_CX_T) Using what you've provided I can see that R_T=R_A(1-B_CX_T)+(X_A+X_L)(B_CR_T) which also brings me closer with XT X_T=R_AB_CR_T+(X_A+X_L)(-1+B_CX_T) If I can just find the sign error now. For...

When I solve for XT I get: X_T={R_T+jX_T \over R_A(-jB_C^2R_T)+(X_A+X_L)(jB_C-B_C^2R_T)} which doesn't seem to be much better than the last attempt. Perhaps you would be willing to show me the transformation to XT=Im as you have described?

Ok I get the basic example you've given as it demonstrates the equality of the real and imaginary parts of two different complex numbers given z1=z2. I am still working towards properly applying that to the separation of the real and imaginary components in the larger expressions. So for...

Ok so after the simplifications that I did, does equating to the real part simply mean to drop all of the remaining imaginary components to arrive at the form of RT that the book author did? Or perhaps to reword my question, does taking the real part of RT at the point where I simplified to...

You are exactly correct. The greater context is a series of equations describing an impedance match using a series inductor and parallel capacitor from RF Circuit Design Theory and Applications where RT is the real part. The example starts off as expressing impedances as real and imaginary...

Homework Statement I am following along in a book which provides the equation below. I have also included the book's stated solution. Homework Equations The Equation: {R_T+jX_T \over 1+jB_C(R_T+jX_T)}+jX_L = R_A-jX_A The Book's Solution: R_T=R_A(1-B_CX_T)+(X_A+X_L)B_CR_T The...

Error was on my part. On the sheet I was using for converting from angular freq. to Hz I neglected to encapsulate /(2*PI()) in one of the locations causing improper order of operations. Problem solved. Thank you both again!

Thank you for your patience and assistance with this. I used your equation, or at least attempted to, when I got those answers. After agreeing with your equation, which I do, I entered it at the location below. 10−12ω2−1=2∗10−6ω It looks right to me which is why I am still confused, but...

-1000000(√2-1) which is f=650645.1423Hz and 1000000(1+√2) which is f=3792237.796Hz when I am expecting ≈384235Hz and ≈65924Hz oddly enough, the above answers seem to be one order of magnitude off with some small additional error, but I am not certain. I am using this formula for...

Ok then I am coming up with ω = 1000000 which is the resonant frequency where XT is infinite, not the -3dB frequency for when XT is +- 50 Ω. Any ideas where I might be going wrong?

I think I am doing this incorrectly. When trying to solve for ω this is what I am getting: |X|= ωL / |1-ω2(LC)| |X - (LCX)ω2| = ωL |-(LCX)ω2| - (L)ω + |X| = 0 I am coming up with ω = 1000000...

Yes the P was meant to be C. Still not quite right yet. Even with your input, the resulting values for X are probably revealing that the formula I provided was not usable this way. I am still working my way though ehild's response as well. When I can correctly solve for ω2 I should at least...

Thank you for this reply but I need to clarify something. I do want to know the angular frequency ω for the given ratio of output voltage to input voltage, but what do you mean by isolate X2 exactly? If X2 is the square a quantity dependent on XC and XL which are both frequency dependent...