High-pass filter output voltage calculation

[dans37buick]

Hello,

I have a question that is on a study guide for a final exam.

In a high-pass filter, Xc = 500 Ω and R=2.2kΩ. What is the output voltage (Vout) when the input voltage (Vin)=10 V.

The given answer is 9.75 /_ 12.8 degrees. I cannot get this answer from my calculations below.

I have calculated it two different ways and come up with two different answers that don't match the given one.

Z= √(500^2+2200^2)=2256.1Ω

10V/2256.1Ω= 4.4 mA

V[SUB][/SUB]r =.0044*2200=9.68 V
V[SUB][/SUB]Xc=.0044*500= 2.2 V

Tan^-1 (2.2/9.68)=12.80

When I plug the numbers into my TI-89 to get the polar coordinates I get 9.92/_12.8 degrees

Second try

10V/2700Ω= 3.7 mA

Vr=.0037*2200=8.14 V
VXc=.0037*500= 1.85 V

Tan^-1 (1.85/8.14)=12.80

When I plug the numbers into my TI-89 to get the polar coordinates I get 8.34/_12.8 degrees

I have been pulling my hair out for the last couple days trying to figure this one out.

Thanks for the help

 

[MikeMl]

Lets do the calculation at 1Hz.

 

[JimB]

Your problem starts here:

10V/2256.1Ω= 4.4 mA

Rounding to 4.4, when you would be better by keeping a few more decomal places:
10/2256.1 = 4.4324

Then 2200 x 4.4324 = 9.7513, which is more like the expected answer.

JimB

 

[dans37buick]

Guess I should have seen that one coming!

Thanks for the help, I thought I was missing a huge step that I could not find in my text.

 

[dans37buick]

Mike I haven't used Spice before we use Multisim at school. Where did you get it, a quick search of the internet didn't reveal much besides lots of files that other people have made.

 

[Winterstone]

Hi,

instead "pulling your hair out for the last couple days" you simply should have checked if your results are exact enough.
Everything OK - except your rounding approach.

The exact current is 4.432 mA and with this value you arrive at the correct voltages Vout=Vr=9.7513 V and |Vxc|=2.216 V.
The corresponding angle is 12.8 deg.


Remark: Right after placing my reply I have noticed: JimB was a bit faster! Congratulation.

 

[MikeMl]

Mike I haven't used Spice before we use Multisim at school. Where did you get it, a quick search of the internet didn't reveal much besides lots of files that other people have made.

Free download at www.Linear.com
Here is a tutorial