Call Search
     

New to Ham Radio?
My Profile

Community
Articles
Forums
News
Reviews
Friends Remembered
Strays
Survey Question

Operating
Contesting
DX Cluster Spots
Propagation

Resources
Calendar
Classifieds
Ham Exams
Ham Links
List Archives
News Articles
Product Reviews
QSL Managers

Site Info
eHam Help (FAQ)
Support the site
The eHam Team
Advertising Info
Vision Statement
About eHam.net

   Home   Help Search  
Pages: [1]   Go Down
  Print  
Author Topic: Basic math  (Read 1429 times)
N3OQD
Member

Posts: 104




Ignore
« on: November 28, 2012, 09:50:25 AM »

There is a question that I was going over with a potential new ham.  It is question G5C07 What is the turns ratio of a transformer used to match an audio amplifier having a 600-ohm output impedance to a speaker having a 4-ohm impedance?
Select   Answer
A   12.2 to 1
B   24.4 to 1
C   150 to 1
D   300 to 1

My math says that "C" is the actual answer but the "correct" one is "A".     In order to use "A" as the correct one my math indicates that the primary should indicate 48.8-Ohms.  So what's up with this?
Logged
KA4POL
Member

Posts: 1901




Ignore
« Reply #1 on: November 28, 2012, 10:06:37 AM »

As you stated correctly, it is impedance that is going to be transformed. This goes by the squareroot and not straight as you assumed. roughly 12.2 is the SQR of 150.
Logged
WB6BYU
Member

Posts: 13010




Ignore
« Reply #2 on: November 28, 2012, 11:25:10 AM »

So the answer is SQRT( 600 / 4 ), or 12.247 : 1

The turns ratio determines the ratio of the voltages.  Say you have a
2 : 1 ratio step-up transformer: with 1V in, you would have 2V out.  Since
the power is the same (assuming a perfect transformer) then the output
current must be half the input.

Ohm's law says R = E / I.  In this case, (2* E) / (I * 0.5) = 4R, which is
why the impedance ratio is the square of the turns ratio, since a turns
ratio of 2 gives an impedance ratio of 4.
Logged
N3OQD
Member

Posts: 104




Ignore
« Reply #3 on: November 28, 2012, 02:51:10 PM »

Yes, I forgot to do the square root of my answer.  Thanks.
Logged
KA4POL
Member

Posts: 1901




Ignore
« Reply #4 on: November 29, 2012, 12:55:51 AM »

It's always good to have some reminder like this one to think about what one usually does without thinking, i.e daily routine.
Logged
W6EM
Member

Posts: 708




Ignore
« Reply #5 on: November 30, 2012, 06:43:33 PM »

The easiest thing to remember to keep it all straight is that power is conserved across an ideal transformer.  Then, as BYU has shown, use low voltage and current examples for the ideal transformer and derive the relationship between primary and secondary.

Brute-force memorization is too much work and can lead to errors.
Logged
Pages: [1]   Go Up
  Print  
 
Jump to:  

Powered by MySQL Powered by PHP Powered by SMF 1.1.11 | SMF © 2006-2009, Simple Machines LLC Valid XHTML 1.0! Valid CSS!