Introduction to Ideal Transformers
concept
Transformers are everywhere. Your house is filled with them, the power supply for your computer, phone, laptop etc have them. The power lines coming into your home have them. The speed controller on your fan might have them (mine does).
A transformer is used to transform AC voltage and current into higher or lower values. Transformers allow you to hook your mains power in your house up to your phone despite the mains power being more than 100V higher than the 5V your phone wants.
In this topic we'll cover the ideal transformer, a model for transformers that is simple enough to not be overwhelming but accurate enough for an introductory AC course.
Our analysis of transformers will assume that all voltages and currents are sine waves. The frequency doesn't matter.
fact
A transformer consists of some magnetic core material around which there are two sets of wires wound around as shown in the illustration below:
The "flux" refers to the magnetic equivalent of current and is how energy is transferred from the primary winding to the secondary winding, don't worry about it for now. More advanced topics on transformers will discuss flux and other such things.
fact
The circuit symbol for the tranformer is show below:
fact
The two windings are called the "primary" winding (the one connected to the voltage source) and the secondary winding (the other one, connected to some kind of load).
fact
The number of turns in the primary winding is called \(N_p\) while the number of turns in the secondary winding is called \(N_s\).
fact
The ratio \(\frac{N_p}{N_s} = n\) is called the "turns ratio".
fact
The voltages and currents in the primary and secondary windings are related by the equations:
$$ \frac{V_p}{V_s} = n $$
$$ \frac{I_s}{I_p} = n $$
As we can see if a transformer increases the voltage it must decrease the current by the same factor.
fact
The input power to the primary side of a transformer is the same as the output power on the secondary side.
This is a consequence of the above facts relating the input and output voltages and currents. Any increase in voltage is always accompanied by a corresponding decrease in current.
fact
We call a transformer whose secondary voltage is higher than the primary voltage a "Step Up" transformer.
A step up transformer will correspondingly lower the input current on the output side.
fact
We call a transformer whose secondary voltage is lower than the primary voltage a "Step Down" transformer.
A step down tranformer will correspondingly increase the input current on the output side.
So a step up transformer has \(0 \lt n \lt 1\)
And a step down transformer has \(n \gt 1\)
practice problems