Question in output transformer

  • Thread starter yungman
  • Start date
  • #1
4,276
44

Main Question or Discussion Point

I am reading audio output transformers. This is a paragraph from RDH4 and I don't understand where the formula of [itex]L_0\;[/itex] come from. Please see attachment.
 

Attachments

Answers and Replies

  • #2
uart
Science Advisor
2,776
9
It looks like it's just [itex]L = \mu \mu_0 N^2 A/l[/itex] where [itex]\mu_0 \simeq 1.26 E-6[/itex] H/m is folded in with the conversion from meters to inches to give the combined constant of 3.2E-8.
 
Last edited:
  • #3
4,276
44
It looks like it's just [itex]L = \mu \mu_0 N^2 A/l[/itex] where [itex]\mu_0 \simeq 1.26 E-6[/itex] is folded in with the conversion from meters to inches to give the combined constant of 3.2E-8.
Thanks for the reply. What is the magnetic path l?

[tex]L_0=\frac {3.2A\mu N^2}{10^8\times l}[/tex]

Also where is 3.2EE2 come from. [itex]\mu_0\;[/itex]=1.256EE-6 won't get 3.2EE2.

Thanks

Alsn
 
Last edited:
  • #4
uart
Science Advisor
2,776
9
Thanks for the reply. What is the magnetic path l?

[tex]L_0=\frac {3.2A\mu N^2}{10^8\times l}[/tex]

Also where is 3.2EE2 come from. [itex]\mu_0\;[/itex]=1.256EE-6 won't get 3.2EE2.

Thanks

Alsn
No, the geometric factor A/l just has units of length. In SI units you use m^2 and m to give A/l in meters. Then of course you use [itex]\mu_0[/itex] in H/m (1.26E-6 H/m).

If however you use inches for A/l then you'll need [itex]\mu_0[/itex] in H/in, so approx divided by 39.4 to give 3.2E-8
 
  • #5
4,276
44
Thanks, so it's just going from meter to inches.

So what is the path length [itesx]l[/itex]? It was given 4.5 inches, where is this come from? Is this the length of the coil?
 
  • #6
uart
Science Advisor
2,776
9
Thanks, so it's just going from meter to inches.

So what is the path length [itesx]l[/itex]? It was given 4.5 inches, where is this come from? Is this the length of the coil?
Yeah, it's the mean flux path length. :smile:
 
  • #7
4,276
44
Thanks Uart, you are of big help.
 
  • #8
4,276
44
Actually I have another question:

We know for solenoid, [itex]B=\mu_0\mu n I\;\hbox{ where n is number of turns per unit length.}[/itex]

So [itex] L=\mu_0\mu n^2 A \;\hbox{ where A is the cross section area of the solenoid.}[/itex]

The equation in the article, N is the total number of turns in the given length. so:

[tex]n=\frac N l\;\Rightarrow\; n^2=\frac {N^2}{l^2}[/tex]

With that [itex]L_0\;[/itex] should be:

[tex] L_0= \frac {3.2A \mu_0\mu}{10^8}\frac{N^2}{l^2}\;\hbox{ instead of }\;L_0= \frac {3.2A \mu_0\mu}{10^8}\frac{N^2}{l}[/tex]
 
  • #9
uart
Science Advisor
2,776
9
With that [itex]L_0\;[/itex] should be:

[tex] L_0= \frac {3.2A \mu_0\mu}{10^8}\frac{N^2}{l^2}\;\hbox{ instead of }\;L_0= \frac {3.2A \mu_0\mu}{10^8}\frac{N^2}{l}[/tex]
No, the equation you post for the solenoid is not for the total inductance, it is for the inductance per unit length. It should read :

[tex]\frac{L}{l}=\mu_0\mu n^2 A [/tex]
 
  • #10
4,276
44
No, the equation you post for the solenoid is not for the total inductance, it is for the inductance per unit length. It should read :

[tex]\frac{L}{l}=\mu_0\mu n^2 A [/tex]
Thanks, do you go to sleep? I put in my sleeping in between these posts and you're still here!!!

So basically the total inductance is take the inductance per unit length times the length:

[tex] L_0= \frac {3.2A \mu_0\mu}{10^8}\frac{N^2}{l^2} \times l \Rightarrow \; L_0= \frac {3.2A \mu_0\mu}{10^8}\frac{N^2}{l}[/tex]
 
  • #11
4,276
44
I have a different question, below is the equivalent circuit from the book: The first image is the part in question about the input impedance. The middle picture is the equivalent circuit at different frequency from the book.

The last picture on the right is my equivalent circuit. The top is the equivalent circuit of the real transformer.
(1) is the equivalent circuit refer to the primary.
(2) is the low frequency equivalent.
(3) is the equation of RA using my equivalent circuit which is different from the book in the first image.
(4) is the high frequency equivalent.

As you can see, the way I draw the equivalent circuit is different from the book, I don't think I can agree with the derivation of the book in the first image on the left. Even the equivalent circuit from the book Handbook of Transformer Design and Application by Flanagan and Wikipedia agree with me as in (1) of my drawing:

http://en.wikipedia.org/wiki/Transformer
 

Attachments

Last edited:
  • #12
4,276
44
Anyone?
 

Related Threads on Question in output transformer

  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
1
Views
3K
  • Last Post
Replies
15
Views
1K
Replies
3
Views
2K
Replies
5
Views
392
Replies
10
Views
1K
  • Last Post
Replies
22
Views
2K
Replies
10
Views
1K
Replies
5
Views
2K
Top