Analyzing transformer circuits

[Walter Harley]

I'd like some help in learning how to analyze circuits that contain
transformers.

The following circuit is the guts of an oscillator in the power supply for a
cheap strobe light. Not shown is another winding (or tap) on the
transformer, from which the ~200V strobe supply is actually derived.

+12V ------o-----o--------.
| | |
.-. | |
3k9 | | --- |
| | --- 10nF |
'-' | |
| | |
o-----o |
| | * |
| '---. ,--'
--- )|(
68nF --- )|(
| .---' '--.
| | * |
'-----o |
| |
--- |
GND ----------v \-------'

(created by Andy´s ASCII-Circuit v1.22.310103 Beta www.tech-chat.de)

I'm trying to understand how to analyze this circuit, e.g., to predict the
frequency of oscillation and the collector voltage and current. I can plug
it into LTSpice (modeling the transformer as two inductors of 1.0mH, ESR=0.5
ohms, mutual inductance 1, phase as shown with asterisks) and it does
approximately what I'd expect. But I couldn't have done it by hand.

What is the right approach to take, with a circuit like this? I'm not
looking for a solution, just some hints on what analysis techniques are
appropriate to use. Thanks for any help.

 

[Robert Baer]

I'd like some help in learning how to analyze circuits that contain
transformers.

The following circuit is the guts of an oscillator in the power supply for a
cheap strobe light. Not shown is another winding (or tap) on the
transformer, from which the ~200V strobe supply is actually derived.

+12V ------o-----o--------.
| | |
.-. | |
3k9 | | --- |
| | --- 10nF |
'-' | |
| | |
o-----o |
| | * |
| '---. ,--'
--- )|(
68nF --- )|(
| .---' '--.
| | * |
'-----o |
| |
--- |
GND ----------v \-------'

(created by Andy´s ASCII-Circuit v1.22.310103 Beta www.tech-chat.de)

I'm trying to understand how to analyze this circuit, e.g., to predict the
frequency of oscillation and the collector voltage and current. I can plug
it into LTSpice (modeling the transformer as two inductors of 1.0mH, ESR=0.5
ohms, mutual inductance 1, phase as shown with asterisks) and it does
approximately what I'd expect. But I couldn't have done it by hand.

What is the right approach to take, with a circuit like this? I'm not
looking for a solution, just some hints on what analysis techniques are
appropriate to use. Thanks for any help.

The transformer inductance, non-linear aspects included if it even
partially saturates, has a lot to do with the frequency of operation.
Transistor turnoff time, due to stored base charge, may be a secondary
consideration.
And, do not forget those capacitors...

 

[Walter Harley]

The transformer inductance, non-linear aspects included if it even
partially saturates, has a lot to do with the frequency of operation.
Transistor turnoff time, due to stored base charge, may be a secondary
consideration.
And, do not forget those capacitors...

Thanks, Robert. I need a bit more help than that, though. I guess what I'm
looking for is some clues as to how to fit transformers into normal analytic
techniques. I learned how to analyze linear circuits back in college,
though I've forgotten most of what I learned; they taught us how to think
about capacitors, resistors, inductors, and active components such as
transistors, but I don't think I ever learned how to cope with transformers.

I apologize; I'm quite ignorant on this topic. The most I've gotten from
the texts I have is that if a current i flows through one winding of a
transformer, then a voltage v will be induced on the other winding such that
v = -M di/dt, where M is the mutual inductance, which in turn equals the
coupling factor k times the square root of the product of the individual
winding's inductances. But I'm not sure how to incorporate that asymmetric
description into a circuit that has independent power sources on both sides
of the transformer, or that has more than two windings. And I'm not sure
how to cope with k < 1 (how do I model the leakage inductances), nor how to
make a realistic estimate of k.

So, help on any of those aspects would be welcome; or, a pointer to a text
that covers this well.

Thanks!