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[Amps] Basic transformer theory

To: <amps@contesting.com>
Subject: [Amps] Basic transformer theory
From: EVonvaltie@aol.com (EVonvaltie@aol.com)
Date: Tue, 7 May 2002 12:05:57 EDT
Sorry - none of you has it right. Here is how it goes:

At no load, the primary sits there drawing a current which is V/X, where X is 
the inductive reactance of the primary. This current is commonly referred to 
as the "magnetizing current". This current will indeed produce a flux density 
and total flux given by the well-known transformer equation. If you analyze 
this formula in detail (which I have done numerous times for my students) you 
will see that the voltage, current and time-integral of the flux are all 
inner related. That is, a given voltage will produce a specific value of 
current with the inductance being the "scale factor". It (inductance) 
contains all of the geometric data for the studied device.

Now, when a load is applied, the secondary current that flows now begins to 
also make an ampere-turn contribution to the total flux, because it shares a 
common core with the primary. This flux then produces a reaction back on the 
primary in the form of an induced voltage that produces an equal and opposite 
flux in the core. With total cancellation, the only remaining core flux and 
primary current is the values that were present with no load. 

This analysis is much easier to visualize if you actually do it formally with 
the correct equations. What you get is a pair of coupled equations for the 
core flux, which have to be solved simultaneously. The result is simply the 
following, as the astute contributors to this discussion have already stated:

       1. The total flux and flux density is invariant with load.
       2. The primary current contains two components: I(magentizing) and 
I(load)
           where the first is simply V/X(L)  and the second is 
V(pri)xN/R(load)

Of course, this is the zero-th order of approximation. In a real power supply 
the resistances and additional core data become significant, and then the 
plot really thickens!

Eric von Valtier  K8LV 


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