# Transformers (Part 2) - Analysis of Transformer Circuits

#### Inductors, Capacitors, Transformers

### Analysis of Transformer Circuits

We finished our discussion of transformer circuits in our last lesson when we were looking at the Zs. We came up with this formula that said the Zp=(Np/Ns)2*Zs. We're going to apply that in a circuit in just a moment but before we do that, I just want to mention a little bit about what is impedance. Impedance is … when we talk about resistance, impedance is a term that is commonly used to talk about resistance in an AC circuit. When you just say resistance, sometimes it can be applied to both. When we talk about impedance, typically we're talking about resistance in an AC circuit.

Let's look at, here have a transformer and a load and we're going to do a few calculations with this. First of all, this is the formula that we just came up with. We said that (Np/Ns)2*Zs would tell us the Zp. As I mentioned earlier, here we have 100 ohms in the secondary. Usually, the secondary resistance or impedance is a known value because you can see it right in the circuit. Let's do some calculations here.

The primary to secondary is a ratio of 10 to one. We would see 10/1 here. The Zs is one. We finished our discussion of transformer circuits in our last lesson when we were looking at the Zs. We came up with this formula that said the Zp=(Np/Ns)2*Zs. We're going to apply that in a circuit in just a moment, but before we do that, I just want to mention a little bit about what is impedance. Impedance is … when we talk about resistance, impedance is the term that is commonly used to talk about resistance in an AC circuit. When you just say resistance, sometimes it can be applied to both. When we talk about impedance, typically we're talking about resistance in an AC circuit.

Let's look at, here have a transformer and a load about 100. Let's see, do we have our calculator handy? If we say 12/100 we're going to get 120mA of current. We'll say 120mA. Let's calculate the power that's dissipated in this transformer. We would say … remember power is E*I. We will say 12v*12mA and let's see, what will that equal? We've got … just a moment here, let me get this back on track here. We would say we have 120mA*12v=1.44W. We have 1.44W.

Now, something we could do, we could take this value and use it to solve for what is the current and power that we have over here. We know that we have 120v applied. We know that we have 1.44W in the secondary. We know that 120v*whatever the current is, is going to equal this value because remember we said that the power in the primary equals the power in the secondary.

If we wanted to solve for I here, we could … well let's see, we could say 1.44W/120v, (120v*I)/120v and then, so we have 1.44W. Now something we could do, we could take this value and use it to solve for what is the current and power that we have over here. We know that we have 120v applied. We know that we have 1.44W in the secondary. We know that 120v*whatever the current is is going to equal this value because remember we said that the power in the primary equals the power in the secondary. If we wanted to solve for I here, we could … well let's see, we could say 1.44W/120v, (120v*I)/120v and then cancel 120v/120v and then I=1.44W/120V. Why don't we do that was our original power calculation?

Okay. We could have done that another way. It would have been a lot simpler actually. We went in and we … remember we went in and we calculated the impedance. We said that is was 10,000. Well, what we could have done, we could have just said 120v/10 [inaudible 0:06:21] and we would have gotten the same value, the 12mA. That would have been a quicker way to do it, but I wanted to walk through it showing the power calculations. But that does prove that our formula here actually does work.

### Impedance of Secondary is Reflected to Primary

Now we've already actually mentioned this. Your text goes into this discussion so I'm going to allude to it. Transformers change voltage and currents depending on turns ratio. It only makes sense that if voltages and currents are impacted, resistance or impedance will also be impacted. The discussion follows on the next slide. Your text goes into the discussion about reflected impedance using the three illustrations to the right. They use these three illustrations. The point of the discussion is that as resistance changes in the secondary, current will also change and this change will be reflected in the primary.

Actually, we re-proved that in that last circuit, but the gist of that is that here they start out with a high resistance. The resistance goes down and then the resistance goes much lower. Well, what's going to happen, as a result of this changing resistance, current is going to increase in the secondary. If the current increases in the secondary then the current must also change in the primary. But the fact is that there's no resistor in the primary. The resistance that is experienced in the primary is a function of the turns ratio and the resistance that you see in the secondary.

As we mentioned here about the … remember how we talked about how the power in the primary causes the power in the secondary. If the secondary current goes up then the primary current must adjust. Okay, so let's do another calculation.

### Transformer Calculations

Here we have … this is a virtual audio transformer. This is one from Workbench. This particular one has a 2:1 ratio. We're showing 169v here. Now that is a peak value. Actually, this is 120v if we consider RMS and this is what you would see out of the wall. That is actually if you measure it with an oscilloscope, that's what you would see as the peak value.

What do we want to do? We want … as a result of this changing resistance, current is going to increase in the secondary. If the current increases in the secondary, then the current must also change in the primary. But the fact is that there's no resistor in the primary. The resistance that is experienced in the primary is a function of the turns ratio and the resistance that you see in the secondary.

As we mentioned here about the – remember how we talked about how the power in the primary causes the power in the secondary. If the secondary current goes up then the primary current must adjust. Okay, let's do another calculation. Here we have … this is a virtual audio transformer. This is one from Workbench. This particular one has a 2:1 ratio.

We're showing 169v here. Now that is a peak value actually … let's see where, there's our calculator and if we say … what have we got, 120/200=600mA. We have 600mA here. If we wanted to calculate the primary power, we would take 120v*600mA. Let's take a quick look at that. 600mA*120v=72W of power. That should be the same thing that we're seeing in the secondary. Let's do our secondary calculation. Let's see. What we have is our voltage and we didn't even talk about the voltage in the secondary, but it's a 2:1 ratio. We have 120v. So it's going to be about 60v in the secondary.

If we take 60v*50?=1.2A and then remember to get power, we'll take that 1.2A*60v=72W. There we have it. We have the 72W in the secondary and 72W in the primary. Now on the next screen, I have … this is actually a MultiSim circuit that you see here. This is the same one that we just looked at right here. You notice the 169v here and the 50?. This is the same circuit.

### MultiSim Simulation

I put a voltmeter in here and these are the actual values that Multisim gave. Notice it's 59.92v. Remember the input was 120v. The turns ratio was 2:1 and so 120v/2=60v. But you'll notice it's fairly close. Multisim is really quite accurate. The turns ratio was … so you would see a little bit of a drop here.

Then we calculated the power and in our calculation, we said that there was 72W. You'll notice here the calculation is very close. That's 71.39W. Now, if you do this simulation actually in MultiSim and you attempt to measure the current in the primary, that simulation that comes with your textbook, the circuits that they have, one of the circuits in this particular chapter … I had great difficulty in getting the multimeter to measure current in the primary. Sometimes simulations don't always work perfectly. What I have here is actually a wattmeter. In your MultiSim package, you do have a wattmeter.

Okay. Next item here.

### Troubleshooting Transformers

In general common defects in transformers are, notice an open primary, an open secondary, shorted turns or shorted windings, windings shorted to the core, short between the primary and the secondary. In fact these four here we had talked about in previous lessons. This is not the only one that's new here, is a short between a primary and a secondary. That will end a transformer. Defects of a transformer can be detected by observation or by checking with an ohmmeter or a voltmeter.

Okay. On this section we looked at … mostly looked at some circuit calculations. In your homework, at the end of the chapter, you'll find you have quite a number of calculations that you can perform to get the feel of transformer calculations.