Coil Transformer
2009
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Coil Transformer
Transformer Concepts
TRANSFORMER CONCEPTS/Jackson Engineering
A step-up transformer has its secondary voltage Vs greater than its primary voltage Vp,
and a step-down transformer has its secondary voltage Vs less than its primary voltage Vp.
This article demonstrates that given a fixed primary voltage Vp, the secondary (step-up or step-down) voltage Vs produced by the transformer is mathematically determined by the number of its primary and secondary windings Np and Ns respectively.
Let's first review some fundamental transformer concepts. Transformers transfer electrical power (energy) from one electrical circuit to another, through its coils. Each primary and secondary coil has a set number of windings (wound about two opposite sides of a magnetic core) Np and Ns respectively.
Through the study of Physics - Electricity & Magnetism, given a fixed primary voltage Vp, a changing current passing through a magnetic cores primary coil winding creates a magnetic field through the cores secondary coil winding. The magnetic field "induces" an electro-magnetic force (emf) or voltage Vs in the secondary winding. This new voltage is called the "induced voltage", and is used to produce the electrical power (current) used in our everyday life.
When a load is connected to the "secondary", electric current flows through the secondary winding. Therefore electrical energy is transferred (transformed using a transformer) from the primary circuit through the transformer to the load.
In an optimal transformer, the induced secondary voltage Vs is proportional
to the fixed primary voltage Vp.
Mathematically this means Vs = (k)(Vp) (where k is the constant of proportionality).
Vs = (k)(Vs) (Equation 1)
It is also true that k equals the ratio of the number of winding turns in the
secondary coil Ns, to the number of winding turns in the primary coil Np.
Mathematically this means k = (Ns)/(Np).
k = (Ns)/(Np). (Equation 2)
Next substituting (Ns)/(Np) for k in (Equation 1) makes Vs = [(Ns)/(Np)][Vp].
Vs = [(Ns)/(Np)] [Vp] (Equation 3)
Next notice that (using Equation 3) since the primary voltage Vp is a fixed voltage, the secondary voltage Vs depends on the number of windings Ns andNpof the transformer.
CASE 1)
By making Ns less than Np, (Ns)/(Np) is less than one. Therefore the secondary voltage Vs is a proper fraction of Vp. This means Vs is stepped-down from Vp. Therefore the secondary step-down voltage Vs produced by the transformer is mathematically determined by the number of its primary and secondary windings Np and Ns respectively.
CASE 2)
By making Ns > Np, (Ns)/(Np) > 1. Therefore the secondary voltage Vs is the product of
Vp and a number greater than one. This means Vs is stepped-up from Vp.
Therefore the secondary step-up voltage Vs produced by the transformer is again mathematically determined by the number of its primary and secondary windings Np and Ns respectively.
In conclusion, by changing Np and Ns with a fixed primary voltage Vp, the secondary
voltage Vs can be changed to a greater or lesser amount from the primary voltage Vp,
hence the terms step-up or step-down transformers.
About the Author
Darren De Marco is a Mathematics professor, and has taught math at CSUN for many years.
How does the relative number of turns on the primary and secondary coil in a transformer affect the step-up?
How does the relative number of turns on the primary and secondary coil in a transformer affect the step-up or step-down voltage factor?
Its been a long time since i did higher physics, but i think its:
As the number of secondry coils increases the voltage gain is increased and the current gain is decreased.
The same for primary but in reverse.
Squer toroidal current transformer coil from Credo-tech
