12. Transformers, Impedance Matching and ... - …

1 12. Transformers, Impedance Matching and Maximum Power TransferIntroductionThe transformer is a device that takes AC at one voltage and transforms it into another voltageeither higher or lower than the original voltage. Alternatively, a transformer can be used to do the samething with current. Transformers only work with AC (and they do not work with DC) because they workon the principle of Faraday's law of induction which involves time varying magnetic flux. Transformersare useful in electronics because (for example) the voltage supplied by the electric utility is 110-120voltages while the voltage used by transistors and integrated circuits is typically a much lower (say 10-12volts).

2 Additionally transformers can be used to isolate a circuit from the ground in which case thetransformer is called an "isolation transformer". Isolation transformer typically have the same number ofturns in the primary and secondary coils since there is no need to increase or decrease the voltage when atransformer is used to isolate a , transformers can also be used to " Impedance match" a power supply with a load tomaximize the power transferred to the load. Power supplies have an internal resistance and even some-thing as simple as a battery has an internal resistance which dissipates part of the power generated.

3 Thispower is wasted since it does not do anything useful. We will show that the maximum power a powersupply to transfer to a load resistor is when the load resistance equals the internal resistance of the powersupply. Unfortunately, often the load resistor does not equal the internal resistance of the power supplybut a transformer can be used to make the effective resistance of the load equal to the power supply andmaximum power transfer is Results of Transformers Theory The basic transformer is two coils wound on an iron core like the diagram of the coils is connected to the AC source of voltage Vp (or current Ip) and this coil is calledthe primary coil.

4 Also suppose the primary coil has Npturns of wire. The load is attached to the sec-ondary coil which we will assume has Ns turns and the voltage across the secondary as measured by avoltmeter is Vs (or an ammeter will measure current Is). The basic transformer equation is(1)VpVs=NpNsand this is easy to remember as the voltage is proportional to the number of turns. Equation (1) is a resultof Faraday's law of induction and this is the reason transformers work only with AC. A transformers iscalled a "voltage step-up transformers" if the secondary voltage Vs is greater than the primary voltage Vs>Vp the ratio of the turns is from equation (1) tells us that Ns>Np.

5 Similarly, a transformers iscalled a "voltage step-down transformers" if the secondary voltage Vs is less than the primary voltage Vs<Vp the ratio of the turns is from equation (1) tells us that Ns<Np. Transformer conserve energy and power (they do not make energy) if they are ideal. Since PowerP=I V it follows that if a transformer is voltage step-up, then it must also be current step down. (Or if thetransformer is voltage step-down, it is current step-up.) The equation for current corresponding toequation (1) is(2)IpIs=NsNpSo the current is inversely proportional to the number of turns.

6 If we are lucky the manufacturer of a transformer publishes the ratio of turns for the transformerr=Np Ns. For example, you might be given that r=2 or the primary has twice the turns as the sec-ondary. Using this with equation (1) you (3)VpVs=rand thus(4)Vs=VprSo for example, if Vp=120 volts the equation (4) tells us that Vs=120/2=60 volts. If we are unlucky and we do not have r the ratio of the turns, we can measure the resistance of theprimary Rp and the resistance of the secondary Rs and assuming the length of the wire is proportional tothe resistance and that the primary and secondary are the same kind of wire (have the same cross sec-tional area) we can conclude(5)r=RpRsThe calculation of equation (3) and (4) follows as before.

7 Mostly the transformers we use have the same kind of wire for the primary and secondary. Infact, the only thing that distinguishes the primary from the secondary of the transformer is which coil isconnected to the voltage source (this will be the primary) and which coil is connected to the load (and thisis called the secondary). For example, the source voltage and load can be reversed in the above trans-former so that the ratio of turns r=1/2 (instead of r=2). Then using equation (3) and (4) with for example,if Vp=120 volts, the equation (4) tells us that Vs= 120 2=240 volts.

8 Either or both the primary and secondary may be "center tapped" which means the primary coilhas a wire running out of the center of the coil. This might be used in constructing certain power supplieslike a full wave power ExercisesPART A: You will be supplied with a transformer and using the resistance argument above togetherwith equation (5), measure the ratio of turns r. Attach your SIGNAL GENERATOR in sine wave modeto the primary and set the amplitude say at 12 volts as measured on your oscilloscope. Attach a loadresistor something like R=5,000 ohms to the secondary and measure the voltage across the load.

9 Useequation (4) to calculate the secondary voltage. Your theoretical prediction should agree pretty muchwith the experiment. PART B: Reverse the voltage source and load as attached to the transformer of PART A. Measure theprimary voltage and secondary voltage and see if the ratio agrees with your prediction from equation (4)and equation (5). PART B: Reverse the voltage source and load as attached to the transformer of PART A. Measure theprimary voltage and secondary voltage and see if the ratio agrees with your prediction from equation (4)and equation (5).

10 PART C: One of the coils of your transformer is probably center-tapped. Measure the resistance fromone end of the coil to the center and see if this is the same as the resistance from the other end to thecenter. If the two resistances are the same it is safe to assume the coil is divided into two equal partshaving the same number of turns. Use the center tapped coil as the secondary and use only half of the coil (that use the part of thecoil from one end to the center). Calculate the ratio of turns r using equation (5). Repeat PART A abovewith the only difference being that you are using only half of the secondary coil.