WEBVTT NOTE Combining Components, and Transformers 1 00:00:00.000 --> 00:00:21.507 One table, and the trap in it. Component, Resistors; Series, add; Parallel, reciprocal. Component, Inductors; Series, add; Parallel, reciprocal. Component, Capacitors; Series, reciprocal; Parallel, add. 2 00:00:21.507 --> 00:00:39.181 Resistors and inductors behave alike. Capacitors are the reverse, and that is the single most reliable trap in this subelement. Two questions the pool asks as a pair: 3 00:00:39.181 --> 00:00:47.301 Question. Which of the following components should be added to a capacitor to increase the capacitance? 4 00:00:48.201 --> 00:00:52.241 Answer. A capacitor in parallel. 5 00:00:52.841 --> 00:01:00.109 Question. Which of the following components should be added to an inductor to increase the inductance? 6 00:01:01.009 --> 00:01:04.434 Answer. An inductor in series. 7 00:01:05.034 --> 00:01:30.396 Read those together and the asymmetry is unmistakable. Working the numbers. Three resistors, 10, 20, 50 ohms, in parallel: 1 / R = 1/10 + 1/20 + 1/50 = 0.1 + 0.05 + 0.02 = 0.17, so R = 5.9 ohms. 8 00:01:30.396 --> 00:01:47.521 Sanity check: smaller than 10, the smallest branch. Always. 100 and 200 ohms in parallel: product over sum = 20000 / 300 = 67 ohms. 9 00:01:47.521 --> 00:02:07.392 Two 5.0 nF capacitors and one 750 pF in parallel: capacitors in parallel add, but convert units first. 750 pF = 0.75 nF, so 5.0 + 5.0 + 0.75 = 10.75 nF. 10 00:02:07.392 --> 00:02:28.701 Three 100 µF capacitors in series: equal components in series divide, so 100 / 3 = 33.3 µF. A 20 µF in series with a 50 µF: product over sum = 1000 / 70 = 14.3 µF. 11 00:02:28.701 --> 00:02:48.702 Three 10 mH inductors in parallel: equal components in parallel divide, 10 / 3 = 3.3 mH. A 20 mH in series with a 50 mH: inductors in series add = 70 mH. 12 00:02:48.702 --> 00:03:16.940 Notice how often equal components appear: three identical parts in series or parallel is simply one part divided by three, whichever rule applies. That shortcut answers half the questions in this group. Transformers. 13 00:03:16.940 --> 00:03:29.380 Question. What causes a voltage to appear across the secondary winding of a transformer when an AC voltage source is connected across its primary winding? 14 00:03:30.280 --> 00:03:33.460 Answer. Mutual inductance. 15 00:03:34.060 --> 00:03:55.263 Changing current in the primary produces a changing magnetic field, which induces a voltage in the secondary. No electrical connection is required or present, which is also why a transformer provides isolation. 16 00:03:55.263 --> 00:04:15.860 Voltage transforms with the turns ratio. (V s ) divided by (V p ) equals (N s ) divided by (N p ) 500-turn primary, 1500-turn secondary, 120 V in: ratio 3:1 up, so 120 times 3 = 360 volts. And in reverse: 17 00:04:15.860 --> 00:04:28.820 Question. What is the output voltage if an input signal is applied to the secondary winding of a 4:1 voltage step-down transformer instead of the primary winding? 18 00:04:29.720 --> 00:04:34.600 Answer. The input voltage is multiplied by 4. 19 00:04:35.200 --> 00:04:51.975 Driving a step-down transformer backwards steps up. A transformer has no preferred direction; the ratio is a property of the windings, and which one you call "primary" is a matter of how you connected it. 20 00:04:51.975 --> 00:04:54.360 Current transforms inversely. 21 00:04:54.360 --> 00:05:05.320 Question. Why is the primary winding wire of a voltage step-up transformer usually a larger size than that of the secondary winding? 22 00:05:06.220 --> 00:05:11.071 Answer. To accommodate the higher current of the primary. 23 00:05:11.671 --> 00:05:27.187 An ideal transformer conserves power. Step the voltage up and the current must come down on the secondary, which means it is higher on the primary, so the primary wire is thicker. 24 00:05:27.187 --> 00:05:39.063 This surprises people who expect the high-voltage side to need the heavier wire. Impedance transforms with the SQUARE of the turns ratio. 25 00:05:39.063 --> 00:05:53.712 (Z p ) divided by (Z s ) equals ((N p ) divided by (N s )) to the power of 2 which gives Because impedance is voltage over current and both change, the effects multiply. 26 00:05:53.712 --> 00:06:04.151 Question. What transformer turns ratio matches an antenna's 600-ohm feed point impedance to a 50-ohm coaxial cable? 27 00:06:05.051 --> 00:06:09.171 Answer. 3.5 to 1. 28 00:06:09.771 --> 00:06:28.371 √(600 / 50) = √12 = 3.46, so about 3.5 to 1. The number to remember: a 4:1 balun transforms 200 ohms to 50, a 4:1 impedance ratio, achieved with a 2:1 turns ratio. 29 00:06:28.371 --> 00:06:51.991 Baluns are named by their impedance ratio, which is exactly the confusion this formula resolves. Check yourself. Two 10 µF capacitors in series. Total? A transformer matches 450 ohms to 50 ohms. Turns ratio? 30 00:06:51.991 --> 00:06:57.126 You need more inductance. Series or parallel? 31 00:07:03.126 --> 00:07:29.126 Capacitors in series use the reciprocal rule; two equal ones halve: 5 µF. √(450 / 50) = √9 = 3:1. Series. Inductors add in series, like resistors, and unlike capacitors.