Transformer, AC Source, and a Battery

[drumercalzone]

Homework Statement

Using an AC signal generator v_s, a transformer with turns ratio n = 1, and a battery V_B, sketch a circuit that will generate the output signal v_out = v_s + V_B

Homework Equations

[tex] \frac{V_2}{V_1} = \frac{N_2}{N_1} [/tex]

The Attempt at a Solution

Here's my sketch, but I feel like I'm missing something conceptually. Because if this were the case, couldn't the battery be on the bottom wire since we're dealing with an AC signal source?

 

[berkeman]

Homework Statement

Using an AC signal generator v_s, a transformer with turns ratio n = 1, and a battery V_B, sketch a circuit that will generate the output signal v_out = v_s + V_B

Homework Equations

[tex] \frac{V_2}{V_1} = \frac{N_2}{N_1} [/tex]

The Attempt at a Solution

Here's my sketch, but I feel like I'm missing something conceptually. Because if this were the case, couldn't the battery be on the bottom wire since we're dealing with an AC signal source?

Looks fine to me. The battery can go in either the bottom or top leg of the secondary. It will still add a DC offset to the output.

 

[drumercalzone]

Thank you for your help! It just seemed too easy!

 

[berkeman]

You are welcome.

One of the things that makes this work in this example, is that the internal resistance of an ideal voltage source is zero. So putting the DC voltage source in series with the transformer does nothing but add an offset voltage.

 

[rwisz]

Your sketch looks correct, but there may be some confusion about the role of the transformer in this circuit. The transformer is used to step up or step down the voltage of the AC signal from the source, but it does not change the nature of the signal itself. In this circuit, the transformer is simply acting as a voltage source with a different voltage level than the AC source.

As for the placement of the battery, it can be on either side of the circuit as long as it is in series with the AC source and the transformer. The key is that the battery is providing a constant DC voltage to the output signal, which is added to the varying AC signal from the source. This creates the desired output signal, vout = vs + VB.

Overall, your understanding of the concept is correct and your sketch accurately represents the circuit. Keep in mind that the transformer is just one component in this circuit and its role is to manipulate the voltage, while the AC source and battery are the main sources of the signal.