Help using complex numbers to work out LRC circuits ???

J

jalbers@bsu.edu

Guest
I am trying to understand XLR circuits and the use of complex numbers
to find solutions. I think that I am applying and interpreting the
math correctly but would feel more comfortable if someone with more
experience took a look at what I am doing...

Suppose that a 50 ohm resistor, 1 mH inductor, and 100 pF capacitor
wired in series are connected to a 1V AC 10Mhz power supply.

Z = 50 + 62.8j – 159j
Z = 50 – 96.2j or 108.417@-62.53

Suppose that I wanted to find the voltage drops across L, R, and C
when the power source is at .707V or 1@45 or .707 + .707j .

I = V/Z or
I = 1@45 / 108.417@-62.53 = .0092@107.53 or -.0027+.0087j
Taking the real part of -.0027+.0087j means that when the voltage
source is at .707 volts, the current through L, R, and C is at -.0027
amps.

The voltage across R:
(50@0) * (.0092@107.53) = .46@107.53 or -.138 + .438j
Taking the real part of -.138 + .438j means that when the voltage
source is at .707 volts, the voltage across R is at -.138 volts.

The voltage across L:
(62.8@90) * (.0092@107.53) = .577@197.53 or -.550 - .173j
Taking the real part of -.550 - .173j means that when the voltage
source is at .707 volts, the voltage across L is at -.550 volts.

The voltage across C:
(159@-90) * (.0092@107.53) = 1.4628@17.53 or 1.394 + .440j
Taking the real part of 1.394 + .440j means that when the voltage
source is at .707 volts, the voltage across L is at 1.394 volts.

------

Any comments or corrections would be greatly appreciated. Thanks
 
<jalbers@bsu.edu> wrote in message
news:e52da699-2f16-49f1-9b8a-f877cf0cf3c0@w1g2000prd.googlegroups.com
I am trying to understand XLR circuits and the use of complex numbers
to find solutions. I think that I am applying and interpreting the
math correctly but would feel more comfortable if someone with more
experience took a look at what I am doing...

Suppose that a 50 ohm resistor, 1 mH inductor, and 100 pF capacitor
wired in series are connected to a 1V AC 10Mhz power supply.

Z = 50 + 62.8j  159j
Z = 50  96.2j or 108.417@-62.53
Click to expand...
Your 62.8j Ohms doesn't look right for a 1 mH inductor
at 10 MHz. I think you "lost" the power of ten multiplier.
Should be more like j62.8K .
 
On Thu, 19 Jun 2008 17:09:46 -0700 (PDT), "jalbers@bsu.edu"
<jalbers@bsu.edu> wrote:

On Jun 19, 4:28 pm, "Greg Neill" <gneill...@OVEsympatico.ca> wrote:
jalb...@bsu.edu> wrote in message

news:e52da699-2f16-49f1-9b8a-f877cf0cf3c0@w1g2000prd.googlegroups.com

I am trying to understand XLR circuits and the use of complex numbers
to find solutions.  I think that I am applying and interpreting the
math correctly but would feel more comfortable if someone with more
experience took a look at what I am doing...

Suppose that a 50 ohm resistor, 1 mH inductor, and 100 pF capacitor
wired in series are connected to a 1V AC 10Mhz power supply.

Z = 50 + 62.8j   159j
Z = 50   96.2j or 108....@-62.53

Your 62.8j Ohms doesn't look right for a 1 mH inductor
at 10 MHz.  I think you "lost" the power of ten multiplier.
Should be more like j62.8K .

The 1 mH means 1 micro henry, not 1 milli henry.
Click to expand...
---
No, it doesn't. In standard scientific notation, the lower case 'm'
stands for 1/1000, not 1/1000000.

In order to eliminate confusion you should either use the symbol 'ľ'
or spell out 'microhenry' if that's what you mean.

JF
 
On Jun 19, 4:28 pm, "Greg Neill" <gneill...@OVEsympatico.ca> wrote:
jalb...@bsu.edu> wrote in message

news:e52da699-2f16-49f1-9b8a-f877cf0cf3c0@w1g2000prd.googlegroups.com

I am trying to understand XLR circuits and the use of complex numbers
to find solutions.  I think that I am applying and interpreting the
math correctly but would feel more comfortable if someone with more
experience took a look at what I am doing...

Suppose that a 50 ohm resistor, 1 mH inductor, and 100 pF capacitor
wired in series are connected to a 1V AC 10Mhz power supply.

Z = 50 + 62.8j   159j
Z = 50   96.2j or 108....@-62.53

Your 62.8j Ohms doesn't look right for a 1 mH inductor
at 10 MHz.  I think you "lost" the power of ten multiplier.
Should be more like j62.8K .
Click to expand...
The 1 mH means 1 micro henry, not 1 milli henry.
 
On Thu, 19 Jun 2008 19:35:14 -0500, John Fields wrote:

On Thu, 19 Jun 2008 17:09:46 -0700 (PDT), "jalbers@bsu.edu"
jalbers@bsu.edu> wrote:

Your 62.8j Ohms doesn't look right for a 1 mH inductor at 10 MHz.  I
think you "lost" the power of ten multiplier. Should be more like
j62.8K .

The 1 mH means 1 micro henry, not 1 milli henry.

---
No, it doesn't. In standard scientific notation, the lower case 'm'
stands for 1/1000, not 1/1000000.

In order to eliminate confusion you should either use the symbol 'Âľ' or
spell out 'microhenry' if that's what you mean.
Click to expand...
To OP: for ease of use in usenet posting, 'u' will do for 'micro', e.g.
'1uH'. The message will be understood. FWIW, when I saw mH, I *assumed*
microhenry, just because it makes more sense, both through understanding
of the construction of inductors, and the application at 10MHz. Still,
it's never a good thing to make assumptions in electric circuits, and
using 'm' for 'micro' is certainly incorrect.
 
On Jun 19, 8:35 pm, John Fields <jfie...@austininstruments.com> wrote:
On Thu, 19 Jun 2008 17:09:46 -0700 (PDT), "jalb...@bsu.edu"





jalb...@bsu.edu> wrote:
On Jun 19, 4:28 pm, "Greg Neill" <gneill...@OVEsympatico.ca> wrote:
jalb...@bsu.edu> wrote in message

news:e52da699-2f16-49f1-9b8a-f877cf0cf3c0@w1g2000prd.googlegroups.com

I am trying to understand XLR circuits and the use of complex numbers
to find solutions.  I think that I am applying and interpreting the
math correctly but would feel more comfortable if someone with more
experience took a look at what I am doing...

Suppose that a 50 ohm resistor, 1 mH inductor, and 100 pF capacitor
wired in series are connected to a 1V AC 10Mhz power supply.

Z = 50 + 62.8j   159j
Z = 50   96.2j or 108....@-62.53

Your 62.8j Ohms doesn't look right for a 1 mH inductor
at 10 MHz.  I think you "lost" the power of ten multiplier.
Should be more like j62.8K .

The 1 mH means 1 micro henry, not 1 milli henry.

---
No, it doesn't.  In standard scientific notation, the lower case 'm'
stands for 1/1000, not 1/1000000.

In order to eliminate confusion you should either use the symbol 'ľ'
or spell out 'microhenry' if that's what you mean.

JF- Hide quoted text -

- Show quoted text -
Click to expand...
I didn't know how to generate the "mu" character and even if I figured
it out I was afraid it wouldn't show up correctly on everyone's
computer so I used m for micro forgetting that m stands for milli like
ma in milli amps. I will spell it out in the furure to avoid any
confusion.

What about the rest of the math that follows ?????????????
 
<jalbers@bsu.edu> wrote in message
news:7ec6fc1a-6b70-403a-873f-3e19a5fc2392@25g2000hsx.googlegroups.com

What about the rest of the math that follows ?????????????
Click to expand...
Check your numbers for the inductor. The angle doesn't
look right.
 
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