Question: [![enter image description here](https://i.stack.imgur.com/UA06h.png)](https://i.stack.imgur.com/UA06h.png)

I have this circuit with both AC and DC supplies and am trying to calculate the voltage at Node A.

Is it possible to simplify the circuit somehow? 

**edit:**  

The voltage will fluctuate 3Vrms above and below the 12V DC. Does that mean that ideally, on the positive half wave, the Zener will cut the top off the sine wave at 5.1v.

Answer: 
> 
> I have this circuit with both AC and DC supplies and am trying to
>  calculate the voltage at Node A.
> 
> 
> 

[![enter image description here](https://i.stack.imgur.com/4l0MD.png)](https://i.stack.imgur.com/4l0MD.png)
![schematic](https://i.stack.imgur.com/aWvde.png)

[simulate this circuit](/plugins/schematics?image=http%3a%2f%2fi.stack.imgur.com%2faWvde.png) – Schematic created using [CircuitLab](https://www.circuitlab.com/)

*Figure 1. Rearrangement of the voltage sources.*

It may help to rearrange the voltage sources as shown in Figure 1. There will be no change at Node A but analysis becomes a little more intuitive.

* The top of BAT1 is held at a constant 12 V.
* If we add a sinusoidal voltage source to that the result is simply the sum of the two voltages: \$ V\_A = V\_{BAT} + V\_{AC} = 12 + 3 sin(100) \$.
* To calculate the peak and minimum remember that the AC signal is RMS and will peak at \$ \sqrt 2 \times 3 \; V \$.

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> 
> The voltage will fluctuate 3 Vrms above and below the 12 V DC. Does that mean that ideally, on the positive half wave, the Zener will cut the top off the sine wave at 5.1 V?
> 
> 
> 

First, consider that you have a voltage divider consisting of Rs and R1. The voltage on R1 will be \$ \frac {R\_1}{R\_S + R\_1}(12 + 3 sin(100)) \$. *This* will be clamped at a maximum of 5.1 V.