WEBVTT NOTE Operational Amplifiers 1 00:00:00.000 --> 00:00:02.380 What an op-amp is. 2 00:00:02.380 --> 00:00:06.824 Question. What is an operational amplifier? 3 00:00:07.724 --> 00:00:19.164 Answer. A high-gain, direct-coupled differential amplifier with very high input impedance and very low output impedance. 4 00:00:19.764 --> 00:00:35.916 Four properties, and the pool asks two of them separately: Very high input impedance, it draws essentially no current from what drives it. Very low output impedance, its output holds its voltage under load. 5 00:00:35.916 --> 00:00:46.971 Very high open-loop gain, typically 100,000 or more. Direct-coupled, it amplifies down to DC. The high gain is not there to be used directly. 6 00:00:46.971 --> 00:00:57.321 It is there so that negative feedback can set the gain precisely with two resistors, and the op-amp's own variation stops mattering. 7 00:00:57.321 --> 00:01:14.032 The inverting amplifier. This question refers to one of the exam's circuit diagrams, which you will need to look at in the written lesson. 8 00:01:14.032 --> 00:01:34.496 A v equals minus (R F ) divided by (R 1 ) Gain is the ratio of two resistors and nothing else. The op-amp's own gain cancels out, which is the whole reason for feedback. 9 00:01:34.496 --> 00:01:57.019 Four worked answers, exactly as the pool asks them: R1, 10 Ω; R_F, 470 Ω; Gain, 470/10 = 47. R1, 1800 Ω; R_F, 68 kΩ; Gain, 68000/1800 = 38. R1, 3300 Ω; R_F, 47 kΩ; Gain, 47000/3300 = 14. 10 00:01:57.019 --> 00:02:23.296 R1, 1000 Ω; R_F, 10 kΩ; Gain, 10, and with 0.23 V in, out is −2.3 V. The minus sign is the inversion. Questions asking for "absolute voltage gain" want the magnitude; the one supplying an input voltage wants the sign. 11 00:02:23.296 --> 00:02:34.557 Non-ideal behaviour. An ideal op-amp is a useful fiction. Three departures from it are asked. 12 00:02:34.557 --> 00:02:41.877 Question. How does the gain of an ideal operational amplifier vary with frequency? 13 00:02:42.777 --> 00:02:46.697 Answer. It does not vary with frequency. 14 00:02:47.297 --> 00:02:51.617 Ideally flat. Really, not: 15 00:02:51.617 --> 00:02:57.337 Question. What is the gain-bandwidth of an operational amplifier? 16 00:02:58.237 --> 00:03:05.397 Answer. The frequency at which the open-loop gain of the amplifier equals one. 17 00:03:05.997 --> 00:03:27.206 Gain-bandwidth product is roughly constant: an op-amp with a 1 MHz GBW gives a gain of 10 up to 100 kHz, or a gain of 100 up to 10 kHz. Gain and bandwidth trade directly, which is why an audio op-amp is useless at RF. 18 00:03:27.206 --> 00:03:33.846 Question. What is meant by the term "op-amp input offset voltage"? 19 00:03:34.746 --> 00:03:42.626 Answer. The differential input voltage needed to bring the open loop output voltage to zero. 20 00:03:43.226 --> 00:03:51.180 Real inputs are not perfectly matched, so a small differential voltage is needed to balance them. 21 00:03:51.180 --> 00:04:07.088 Multiplied by the closed-loop gain, offset appears as a DC error at the output, which matters in a DC-coupled instrumentation circuit and not at all in an audio one. Adding a feedback capacitor. 22 00:04:07.088 --> 00:04:17.168 Question. What is the frequency response of the circuit in E7-3 if a capacitor is added across the feedback resistor? 23 00:04:18.068 --> 00:04:21.516 Answer. Low-pass filter. 24 00:04:22.116 --> 00:04:32.544 The capacitor's reactance falls as frequency rises, so the effective feedback impedance falls, so the gain falls, a low-pass response. 25 00:04:32.544 --> 00:04:43.906 It is the standard way to roll off an op-amp stage above the frequencies you care about, and it also tames the stability problem below. Stability. 26 00:04:43.906 --> 00:04:52.986 Question. How can unwanted ringing and audio instability be prevented in an op-amp audio filter? 27 00:04:53.886 --> 00:04:58.446 Answer. Restrict both gain and Q. 28 00:04:59.046 --> 00:05:09.932 An active filter with high gain and high Q is close to oscillating: the ringing you hear on a transient is that near-oscillation. 29 00:05:09.932 --> 00:05:21.155 Both parameters have to be kept modest, and if you need a sharp response, cascade several gentle stages rather than pushing one hard. 30 00:05:21.155 --> 00:05:36.007 This is the same trade as the antenna Q lesson, high Q, narrow response, and ringing on anything that changes quickly. Check yourself. R1 = 2.2 kΩ, R_F = 100 kΩ. Absolute gain? 31 00:05:36.007 --> 00:05:49.846 An op-amp has a 4 MHz gain-bandwidth product. What is its usable bandwidth at a gain of 20? Your active audio filter rings on speech transients. What do you adjust? 32 00:05:55.846 --> 00:06:16.379 100000 / 2200 = 45.5. 4 MHz / 20 = 200 kHz. Reduce gain and Q. If you need the sharpness, cascade gentler stages.