15.6 Transformers  (Page 2/9)

Combining the last two equations, we have

Hence, with appropriate values for $N_{\text{S}}\text{and}{N}_{\text{P}},$ the input voltage $v_{\text{P}}(t)$ may be “stepped up” $\left(N_{\text{S}}>N_{\text{P}}\right)$ or “stepped down” ( $N_{\text{S}}<N_{\text{P}}$ ) to $v_{\text{S}}(t),$ the output voltage. This is often abbreviated as the transformer equation    ,

which shows that the ratio of the secondary to primary voltages in a transformer equals the ratio of the number of turns in their windings. For a step-up transformer    , which increases voltage and decreases current, this ratio is greater than one; for a step-down transformer    , which decreases voltage and increases current, this ratio is less than one.

From the law of energy conservation, the power introduced at any instant by $v_{\text{P}}(t)$ to the primary winding must be equal to the power dissipated in the resistor of the secondary circuit; thus,

When combined with [link] , this gives

If the voltage is stepped up, the current is stepped down, and vice versa.

Finally, we can use $i_{\text{S}}(t)=v_{\text{S}}(t)\text{/}{R}_{\text{S}}$ , along with [link] and [link] , to obtain

which tells us that the input voltage $v_{\text{P}}(t)$ “sees” not a resistance $R_{\text{S}}$ but rather a resistance

Our analysis has been based on instantaneous values of voltage and current. However, the resulting equations are not limited to instantaneous values; they hold also for maximum and rms values.