Welcome to this web lecture on power gain, part one. In this web lecture, we're going to discuss the concept of power transfer. My name is Domine Leenaerts. The objective of this lecture is to introduce power transfer in the system and to explain the difference between available power, delivered power and dissipated power. And in the end to define power gain. Consider a generic system S. It can be an RF amplifier or a mixer, doesn't matter too much. This system S is driven by a generator consisting of V of S and an internal impedance Z of S. And the system S is loaded by load Z of L. Note that we do not discuss the inside of system S. We consider it as a black box. But we know that the system S has an input impedance ZI and an output impedance ZO. Now let's discuss power transfer and the importance of matching. On the right hand side we see an example where we have a 50 ohm microstripline on the PCB connected to a 50 ohm microstripline on the copper substrate fire and bondwire. In the movie, the color red represents a high strength of energy and the color blue the lowest. What we observe is that the voltage source pulls energy, bounce back on the bondwire and basically will not enter the PCB. That in itself is strange, as we have 50 ohm connected to 50 ohm simply by a piece of metal. However, this piece of metal acts as an inductor, therefore represents an impedance and consequently we have an impedance mismatch between the two 50 ohm striplines. And as a consequence we have basically no energy passing this bondwire. We have a huge mismatch. Now let's discuss available power from a source. Available power is defined as the signal power that would be extracted from a source fee of S by a load conjugately matched to the output of the source. In our example, if we consider resistances rather than impedances, we have the available power as the voltage S to the square divided by four times the internal impedance RFS. That is the maximum power available from the source which we can deliver to system S. The question actually is, how much are we going to deliver to the system S and that depends on the input impedance of the system. The input impedance together with the internal resistance of the generator will cause an voltage division across the input of system S. And as a consequence the power delivered to the system is a function of the two resistances, and of course the source itself. But we can see that the power delivered to the system is smaller or at most equal to the power available from the generator. Let's consider a simple example. Here we have a generator consisting of 10 Volt with an internal impedance of 50 ohm. It's driven an amplifier with an input impedance Rinput. Now, by definition, the available power is of course in half watt. The deliver power is plotted on the right hand side as function of the input impedance itself. And we see that it reaches its maximum at the moment that the Rinput is equal to R of S. In other words, impedance matching between the generator and the amplifier. An available power is really delivered to the system, they are equal. It's also important to understand the difference between power delivered and power dissipated. Let's consider our example again and assume that the Rinput is 50 ohm but the wire connection between the generator and the amplifier we consider as one ohm. Now again, the available power is in half Watt, nothing changes there. The delivered power, however, is now as a consequence of the one ohm wire connection point four nine watt. The dissipated power is the difference between the available power and the delivered power, and can be found as ten milliwatts and is dissipated in the one ohn resistance of the wire. Of course we can also discuss power transfer using waves. We have incident wave and reflected wave. And in this example we have a generator with a complex impedance ZS. And it's loaded by a complex opinion set of L. The available power is now found as the absolute value of the incident wave to the square. And by simply calculation we find that it is equal to the absolute value of E of S to describe the fiber four times R of S, which is exactly the formula we found earlier. And again available power is found at the moment ZL is ZS, optimal power transfer, optimal impedance matching. The deliver power we can also find as a function of the difference between the incident wave and the reflected wave. That's the top formula. Or we find it as an expression with reflection parameter comma P. In both cases, again, it's a function of the ratio between the two impedances as we found earlier. Now we have defined all these available power, deliver power and power transfer, we can define the definitions of power gain and there are four actually. We have first of all the available power gain which found as the available power at the output of our system divided by the available power from the source. And takes therefore into account the mismatched condition at the input of our system. Deliver power, however, is the ratio between the deliver power at the output divided by the delivered power at the input of the system, and takes therefore into account the mismatched conditions at the output. Maximum power gain is defined as the ratio between the out power at the output available divided by the power delivered at the input. It is the maximum power gain we can find. And is purely related to the system S. Transducer power gain is the most realistic power gain, and is the ratio between the power delivered to the load divided by the power available from the source and takes therefore into account mismatched conditions at the input as well as at the output. In summary, transfer of power is influenced by impedance matching conditions. Think of the movie again. We have discussed the concept of available power, deliver power and dissipated power. I mean yes, we defined the definition of power gain, which are basically defined on, based on the transfer of power from a source to a load and we found four definitions of power gain. So, in microwave engineering it's meaningless to speak of gain in itself. You need to be precise in what you defined by gain. Available power gain, deliver power gain, maximum power gain or transducer power gain.
