ENSC2003 - Lecture 17

ENSC2003 - Lecture 16
Transformers - Slides

Transformers $-$ AC device used to change high voltage + low current to low voltage + high current and vice-versa without changing $f$
$\frac{V _{s}}{V _{p}} = \frac{N _{s}}{N _{p}} = \frac{i _{p}}{i _{s}} = n$
Turn ratio ( $n$ ) $-$ ratio of the number of turns between primary and secondary winding
- $n > 1 =$ step up transformer
- $n < 1 =$ step down transformer

The Ideal Transformer - Slides
Slides 42 & 50 required knowledge, slides 43-49 not needed

Current in each coil generates flux that links with other coil
- How do we quantify the flux’s direction?
Position dot shows whether the direction of winding of each coil are in same or opposite directions:

a) fluxes set up are additive, mutual inductance term is +ve
- Positive $v_{1}$ → positive $v_{2}$
  b) fluxes set up are in opposition, mutual inductance terms are -ve
- The voltage would actually have flipped sign for (b)
- Because of how voltage is defined above, $v_{2 b}$ would be negative
If current enters one dot, it must leave the other dot and vice-versa

Dots are aligned $-$ voltages have same direction
Dots misaligned $-$ voltages have different signs

Given example setup below:
- Primary winding power: $P_{1} = v_{1} i_{1}$
- Secondary winding power: $P_{2} = v_{2} i_{2}$
For ideal transformer, no net power supplied to the transformer:
$P = P_{1} + P_{2} = 0$

An ideal transformer can make a load impedance appear larger or smaller when viewed from the other side of the transformer

This is known as impedance transformation
- $\overline{Z} = \frac{V}{I}$ → transformers change voltage and current
- Thus, effective impedance can change through a transformer
  $\overline{Z_{in}} = \frac{1}{n ^{2}} \overline{Z_{L}}$

Maximum power transfer occurs when:
$\overline{Z_{in}} = \overline{Z_{S}}^{*}$
$\overline{Z_{L}}^{*}$ is the complex conjugate of the

Often that real load doesn’t equal source impedance
We use a transformer to transform the load into desired value
Using this equation $\overline{Z_{in}} = \frac{1}{n ^{2}} \overline{Z_{L}}$ :
- Find $n$ and choose a transformer with the correct turn ratio
- You must balance both real and imaginary components of $\overline{Z}$
  - Do both separately using the same equation
- To offset a capacitor, use an inductor and vice-versa

What happens to open/short circuits on the other side of a transformer?

Open circuit still seen as open circuit ( $R \to \infty$ )
- $R$ can never truly be $\infty$ , always will be some very high resistance
- However, if $n >> 1$ , the very large resistance $R$ could be seen as a small value of $R_{in}$ and circuit cannot be treated as open
Short circuit still seen as short circuit ( $R \to 0$ )
- $R$ can never truly be $0$ , always will have some small resistance
- However, if $n << 1$ , the very small value $R$ could be seen as a significant value of $R_{in}$ and circuit cannot be treated as short

ENSC2003 - Lecture 18

Quartz 5