Circuit analysis homework - LTspice results are different from calculations

Original question: I have already tried calculating it, but after simulating the circuit in LTspice, the answer is different.

My working is shown below.

I've included a screenshot of the LTspice showing a Vout of about 118 mV whereas I calculated 1.163 V.   (Original copy of working is at: https://notability.com/n/1r9BP36Zt507ijpb2LnVdc
(Scroll down to page 12))

• For the future, LTspice accepts m as milli, n as nano, k as kilo, etc, so you can avoid writing the values as 0.00...0047, which is hard to read, and write, instead, 47n. Also, if you need accurate frequency analysis then your best bet is to use the .AC analysis, not .TRAN. For a single frequency use .ac list <frequency_value> (e.g. .ac list 100). Don't forget to use labels for nets (F4) so that the readings are much easier. Dec 27 '21 at 10:16
• Thankss! I tried it but I keep getting 0 Vo, here's a snap imgur.com/a/N881vrS Dec 27 '21 at 11:10
• For some reason imgur won't open it, but this is how it should look like. You can also use the .step command for more than one frequency, or add more frequencies in the list: .ac list 100 1k 10k 100k. Dec 27 '21 at 11:37
• ooohh, myh bad, i was using the voltage source in sine mode, got it now. Thanks Dec 27 '21 at 11:41 @100Hz

I get

Za = 4.7000e+03 + 6.2832e+01i

Zb = 2.2000e+03 - 3.3863e+04i

Zc = 1.0000e+03 - 1.5915e+05i

Zp = Za || Zb = 4.5887e+03 - 5.6789e+02i

Vo = 4 * Zp/(Zp + Zc) = 0.0182 + 0.1143i

|Vo| = 0.1157V

• Thanks! But can you please tell me what that e is? I don't understand that representation. It doesn't look like exponential form of complex numbers either. Also why is Vo = 4 * Zp/(Zp + Zc)? Edit: Just realised thats the voltage divider rule. Dec 27 '21 at 9:55
• 4.7000e+03 +6.2832e+01i = 4700 + j * 62.832 It's a commonly used notation. 4V is the input voltage and the rest is just the voltage divider equation. Dec 27 '21 at 9:57
• Thank youuuuu!!! Dec 27 '21 at 10:46
• Hey, do you have any idea about the last part? Here's my graph for part b imgur.com/a/ays3kTe Dec 27 '21 at 16:53
• Since you have already entered it into LTspice, I suggest running an AC analysis. With linear y axis you should get something like this Dec 27 '21 at 17:06

In case you need all others answers for verifying ... Maple sheet. And this for the last question ... • Thanks! There's 1 thing I dont understand. For 100Hz, we got 0.1157V which is ther in your answer, but there's another set of complex number before that, 0.01822042999 + 0.11427...I. What is this? Dec 27 '21 at 11:14
• On lines, First number is the complex answer (a+jb), after you find modulus and then phase in degree ... the answer you want (modulus) is for 100 Hz -> 0.1157228760, then 80.94... degree. Dec 27 '21 at 11:50
• Oh I see, makes sense thanks! Dec 27 '21 at 13:46