Trying to analyze a half wave rectifier with inductor and DC source

AI Thread Summary
The discussion revolves around analyzing a half wave rectifier with an inductor and DC source, focusing on the mathematical equations presented in the book "Power Electronics" by Daniel Hart. Participants express confusion over the algebraic transition from the second to the third equation, particularly regarding the placement of the variable w in the equations. There is a consensus that the current will not be sinusoidal due to the DC voltage biasing the diode. Some users suggest that there may be a typo in the equations, and one participant notes that integrating with respect to time rather than substituting wt resolves the issue. The conversation highlights the complexities of circuit analysis and the importance of accurate mathematical representation.
Jason06841
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TL;DR Summary
I am trying to analyze a half wave rectifier with an inductor and DC source load.
I am trying to analyze a half wave rectifier with an inductor and DC source load. I understand the circuit but I guess I do not get the math. I am reading a book and this is the circuit and equations they came up with. I understand how they got from the first equation to the second equation but I do not understand their algebra to get from the second equation to the third. Shouldn't it be w/L instead of 1/wL? How do they get to the third equation?

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Looks as if the final equation is correct but I do not understand Eq 2.
It also looks to me that the current will not be sinusoidal, as the DC voltage biases the diode beyond cut off for part of the cycle.
 
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Jason06841 said:
TL;DR Summary: I am trying to analyze a half wave rectifier with an inductor and DC source load.

I am reading a book and this is the circuit and equations they came up with.
Give us a link and page number please.
 
tech99 said:
Looks as if the final equation is correct but I do not understand Eq 2.
It also looks to me that the current will not be sinusoidal, as the DC voltage biases the diode beyond cut off for part of the cycle.
These are just the equations for when the diode is forward biased. Starting from Vdc+ to partly into the negative half cycle due to the energy stored in L.

He does a few things there from equation 1 to equation 2. First he redefines the domain from t to wt. Because that would make the lower differential d(wt). But w is constant (in this case) so he is able to pull it out and multiply it by dt and continue to solve the equation in terms of t. However, that puts the w in the denominator so when you rearrange you get w/L instead of what he got which was 1/wL.
 
Jason06841 said:
I am reading a book and this is the circuit and equations they came up with.
Some of us want to know the title, author and ISBN, so we can peruse that chapter.

It seems;
To get from eqn(1) to eqn(2), multiply the rhs by w/w = 1;
Then subtract Vdc from both sides of eqn(2).
Knowing; ZL = w⋅L ;
Eqn(3) is Ohms law, with i = v / ZL.
 
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Baluncore said:
Some of us want to know the title, author and ISBN, so we can peruse that chapter.
Page 5 of the pdf he linked to...
 
Baluncore said:
Some of us want to know the title, author and ISBN, so we can peruse that chapter.

It seems;
To get from eqn(1) to eqn(2), multiply the rhs by w/w = 1;
Then subtract Vdc from both sides of eqn(2).
Knowing; ZL = w⋅L ;
Eqn(3) is Ohms law, with i = v / ZL.
The units in equation 2 and 3 do not balance.

Since i(t) and i(wt) are both the same dimension (elec. current) You don't put an omega inside the argument of function i, then just divide by omega to "cancel out". So yes that's correct to get the derivative to work out, but you need to divide the other side of the equation by omega as well.
 
Baluncore said:
Some of us want to know the title, author and ISBN, so we can peruse that chapter.

It seems;
To get from eqn(1) to eqn(2), multiply the rhs by w/w = 1;
Then subtract Vdc from both sides of eqn(2).
Knowing; ZL = w⋅L ;
Eqn(3) is Ohms law, with i = v / ZL.
Power Electronics, Daniel Hart, ISBN 978-0-07-338067-4
 
  • #10
scottdave said:
The units in equation 2 and 3 do not balance.

Since i(t) and i(wt) are both the same dimension (elec. current) You don't put an omega inside the argument of function i, then just divide by omega to "cancel out". So yes that's correct to get the derivative to work out, but you need to divide the other side of the equation by omega as well.
I do not think he is putting that w in the denominator simply to "cancel out". When he replaces t with wt he ends up with di(wt)/d(wt). Because w is a constant, it becomes di(wt)/wdt but because w is in the denominator on the rhs of equation (2) after rearranging, it should turn up in the numerator in equation (3) but for him it ends up in the denominator.
 
  • #11
Jason06841 said:
I do not think he is putting that w in the denominator simply to "cancel out". When he replaces t with wt he ends up with di(wt)/d(wt). Because w is a constant, it becomes di(wt)/wdt but because w is in the denominator on the rhs of equation (2) after rearranging, it should turn up in the numerator in equation (3) but for him it ends up in the denominator.
Yes, definitely a typo.
 
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  • #12
Turns out if I do not substitute wt and just integrate w.r.t. time it all comes out when I substitute wt at the end after I get my final result. Thanks everyone for your help. If anyone knows the proper way he should have done that substitution please post a reply. I have added a LTSpice plot and circuit if anyone is interested. The green is the voltage at the top of the inductor the red is the current through the inductor.

ltspice.png
 
  • #13
This (in the book you showed) is the kind of Algebra one uses when trying to obtain a desired result. Avoid the book.
 
  • #14
Holy crap! I just clicked into this thread randomly and read the last few posts, and I, um, need to close it temporarily for, um, time for Mentor review. Lordy! :oops:
 
  • #15
Okay, after cleaning up an off-topic dangerous discussion, this thread is now reopened. Have a nice day.
 
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