[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.29,0:00:04.89,Default,,0000,0000,0000,,>> Now, let's go back to our original problem and suppose that we want to design
Dialogue: 0,0:00:04.89,0:00:10.57,Default,,0000,0000,0000,,our output voltage to a be a linear combination of our input voltage and a constant.
Dialogue: 0,0:00:10.58,0:00:13.80,Default,,0000,0000,0000,,Refer to table four dash three in your book,
Dialogue: 0,0:00:13.80,0:00:17.86,Default,,0000,0000,0000,,and this will show you various Op-amp circuits that you already know how to design.
Dialogue: 0,0:00:17.86,0:00:20.13,Default,,0000,0000,0000,,Inverting summers, non-inverting summers,
Dialogue: 0,0:00:20.13,0:00:22.76,Default,,0000,0000,0000,,inverting and non-inverting amplifiers,
Dialogue: 0,0:00:22.76,0:00:26.04,Default,,0000,0000,0000,,subtracting amplifiers and voltage followers, or buffers.
Dialogue: 0,0:00:26.04,0:00:30.48,Default,,0000,0000,0000,,Let's figure out how to use these to design the systems that we want to build.
Dialogue: 0,0:00:30.48,0:00:34.54,Default,,0000,0000,0000,,To do this, I've developed a set of system and circuit design cards.
Dialogue: 0,0:00:34.54,0:00:37.53,Default,,0000,0000,0000,,One side of the card is the system side,
Dialogue: 0,0:00:37.53,0:00:39.52,Default,,0000,0000,0000,,that tells us what operation is needed.
Dialogue: 0,0:00:39.52,0:00:42.06,Default,,0000,0000,0000,,In this case, we would have a multiplier.
Dialogue: 0,0:00:42.06,0:00:44.36,Default,,0000,0000,0000,,That's a non-inverting amplifier where
Dialogue: 0,0:00:44.36,0:00:48.35,Default,,0000,0000,0000,,our input voltage is multiplied by some number greater than one,
Dialogue: 0,0:00:48.35,0:00:51.41,Default,,0000,0000,0000,,to give us the output voltage, right here.
Dialogue: 0,0:00:51.41,0:00:54.29,Default,,0000,0000,0000,,On the other side of the card is the circuit side.
Dialogue: 0,0:00:54.29,0:00:56.39,Default,,0000,0000,0000,,This is the part that you would actually build.
Dialogue: 0,0:00:56.39,0:00:59.66,Default,,0000,0000,0000,,The part that is shown on the front is the area that's within
Dialogue: 0,0:00:59.66,0:01:05.67,Default,,0000,0000,0000,,this blue dashed line here and that shows you the design for a non-inverting amplifier.
Dialogue: 0,0:01:07.67,0:01:11.46,Default,,0000,0000,0000,,So, here are two other system and circuit design cards.
Dialogue: 0,0:01:11.46,0:01:12.57,Default,,0000,0000,0000,,Here's the system side,
Dialogue: 0,0:01:12.57,0:01:14.08,Default,,0000,0000,0000,,here's the circuit side.
Dialogue: 0,0:01:14.08,0:01:16.49,Default,,0000,0000,0000,,There's the non-inverting amplifier that you're used to,
Dialogue: 0,0:01:16.49,0:01:20.66,Default,,0000,0000,0000,,here's an inverting amplifier where we multiply by a negative number.
Dialogue: 0,0:01:20.66,0:01:25.13,Default,,0000,0000,0000,,While we're at it, let's also take a look at the very important input,
Dialogue: 0,0:01:25.13,0:01:27.62,Default,,0000,0000,0000,,resistances for these circuits.
Dialogue: 0,0:01:27.62,0:01:29.70,Default,,0000,0000,0000,,When I look into this circuit,
Dialogue: 0,0:01:29.70,0:01:31.64,Default,,0000,0000,0000,,I'm going to run up against
Dialogue: 0,0:01:31.64,0:01:35.13,Default,,0000,0000,0000,,the input resistance of the Op-amp which we know is very high.
Dialogue: 0,0:01:35.13,0:01:40.68,Default,,0000,0000,0000,,So, Rin for a non-inverting amplifier is approximately equal to infinity.
Dialogue: 0,0:01:40.68,0:01:43.19,Default,,0000,0000,0000,,But when I look into the inverting amplifier,
Dialogue: 0,0:01:43.19,0:01:45.16,Default,,0000,0000,0000,,I know it looks infinite in this direction,
Dialogue: 0,0:01:45.16,0:01:49.31,Default,,0000,0000,0000,,but my current is able to follow this path right here,
Dialogue: 0,0:01:49.31,0:01:55.26,Default,,0000,0000,0000,,which means that it is not going to have an infinite input resistance.
Dialogue: 0,0:01:55.26,0:01:56.72,Default,,0000,0000,0000,,So, in this case,
Dialogue: 0,0:01:56.72,0:01:58.82,Default,,0000,0000,0000,,it's not equal to infinity.
Dialogue: 0,0:01:58.82,0:02:03.78,Default,,0000,0000,0000,,That means I probably don't need a buffer if I'm doing a non-inverting amplifier,
Dialogue: 0,0:02:03.78,0:02:10.05,Default,,0000,0000,0000,,but I do need a buffer right here if I am doing an inverting amplifier.
Dialogue: 0,0:02:10.34,0:02:15.11,Default,,0000,0000,0000,,Here are two summers, the system design card and the circuit design card.
Dialogue: 0,0:02:15.11,0:02:18.06,Default,,0000,0000,0000,,Again, let's take a look at the input resistance.
Dialogue: 0,0:02:18.06,0:02:20.18,Default,,0000,0000,0000,,When I look into the inverting summer,
Dialogue: 0,0:02:20.18,0:02:23.34,Default,,0000,0000,0000,,is that input resistance infinity? No, it isn't.
Dialogue: 0,0:02:23.34,0:02:25.86,Default,,0000,0000,0000,,Rin is not equal to infinity,
Dialogue: 0,0:02:25.86,0:02:30.04,Default,,0000,0000,0000,,so plan to use a buffer if you're using an inverting summer.
Dialogue: 0,0:02:30.04,0:02:33.08,Default,,0000,0000,0000,,When I look into the non-inverting summer however,
Dialogue: 0,0:02:33.08,0:02:35.27,Default,,0000,0000,0000,,that input resistance is close to
Dialogue: 0,0:02:35.27,0:02:39.61,Default,,0000,0000,0000,,infinity and so I won't be needing a buffer for that device.
Dialogue: 0,0:02:39.61,0:02:42.72,Default,,0000,0000,0000,,Here's another system and circuit design card.
Dialogue: 0,0:02:42.72,0:02:44.96,Default,,0000,0000,0000,,This is a differencing amplifier,
Dialogue: 0,0:02:44.96,0:02:48.14,Default,,0000,0000,0000,,where I will multiply both of my voltages by a constant,
Dialogue: 0,0:02:48.14,0:02:49.64,Default,,0000,0000,0000,,but then I will subtract them.
Dialogue: 0,0:02:49.64,0:02:52.53,Default,,0000,0000,0000,,Here's how I designed that system.
Dialogue: 0,0:02:53.06,0:02:57.36,Default,,0000,0000,0000,,Switches are other important things that Op-amps are able to do.
Dialogue: 0,0:02:57.36,0:03:01.46,Default,,0000,0000,0000,,Remember we talked about a single-pole double-throw switch in an example
Dialogue: 0,0:03:01.46,0:03:07.42,Default,,0000,0000,0000,,previously where my Op-amp railed out between Vcc and minus Vcc.
Dialogue: 0,0:03:07.42,0:03:11.15,Default,,0000,0000,0000,,That's the equivalent of doing a single-pole double-throw switch.
Dialogue: 0,0:03:11.15,0:03:16.61,Default,,0000,0000,0000,,Here's a single-pole single-throw switch where it goes between Vcc and ground.
Dialogue: 0,0:03:16.61,0:03:21.12,Default,,0000,0000,0000,,Here's the system design card and here's how you build the circuit.
Dialogue: 0,0:03:21.59,0:03:25.10,Default,,0000,0000,0000,,Now, a buffer of course is a very important part of many of
Dialogue: 0,0:03:25.10,0:03:27.89,Default,,0000,0000,0000,,our circuits and that's because I'm able to buffer
Dialogue: 0,0:03:27.89,0:03:33.32,Default,,0000,0000,0000,,the input and output resistances of various devices so that I can design them separately.
Dialogue: 0,0:03:33.32,0:03:34.68,Default,,0000,0000,0000,,That's the key idea.
Dialogue: 0,0:03:34.68,0:03:37.03,Default,,0000,0000,0000,,Here is the symbol we often use for a buffer.
Dialogue: 0,0:03:37.03,0:03:40.52,Default,,0000,0000,0000,,A buffer is a unity gain amplifier where we simply multiply
Dialogue: 0,0:03:40.52,0:03:44.88,Default,,0000,0000,0000,,our input value by one in order to get our output voltage.
Dialogue: 0,0:03:44.88,0:03:46.63,Default,,0000,0000,0000,,This is the system design card,
Dialogue: 0,0:03:46.63,0:03:49.74,Default,,0000,0000,0000,,here's the circuit design card that shows us how to build it.
Dialogue: 0,0:03:49.74,0:03:52.73,Default,,0000,0000,0000,,We simply connect the negative terminal,
Dialogue: 0,0:03:52.73,0:03:57.74,Default,,0000,0000,0000,,the negative input to the output terminal and that gives us a gain of one.
Dialogue: 0,0:03:57.74,0:04:00.26,Default,,0000,0000,0000,,When I look into the input of a buffer,
Dialogue: 0,0:04:00.26,0:04:04.92,Default,,0000,0000,0000,,I can see that I'm going up against the input resistance of the Op-amp,
Dialogue: 0,0:04:04.92,0:04:07.90,Default,,0000,0000,0000,,so, Rin for a buffer is always
Dialogue: 0,0:04:07.90,0:04:12.24,Default,,0000,0000,0000,,approximately equal to infinity and that's why we like them so well.
Dialogue: 0,0:04:12.56,0:04:15.74,Default,,0000,0000,0000,,So, let's talk about an example where we might want
Dialogue: 0,0:04:15.74,0:04:18.45,Default,,0000,0000,0000,,to do a linear combination of voltages.
Dialogue: 0,0:04:18.45,0:04:21.05,Default,,0000,0000,0000,,Perhaps these four voltages came from a series
Dialogue: 0,0:04:21.05,0:04:23.48,Default,,0000,0000,0000,,of sensors and some of them we really trust,
Dialogue: 0,0:04:23.48,0:04:25.97,Default,,0000,0000,0000,,we want to multiply them by a large number,
Dialogue: 0,0:04:25.97,0:04:27.53,Default,,0000,0000,0000,,and some we don't trust quite as much,
Dialogue: 0,0:04:27.53,0:04:29.87,Default,,0000,0000,0000,,we want to multiply them by a small number.
Dialogue: 0,0:04:29.87,0:04:35.24,Default,,0000,0000,0000,,So, here's the equation that we might like to have in order to get our output voltage.
Dialogue: 0,0:04:35.24,0:04:37.44,Default,,0000,0000,0000,,There are many ways we could build this circuit.
Dialogue: 0,0:04:37.44,0:04:38.96,Default,,0000,0000,0000,,We could add things up first,
Dialogue: 0,0:04:38.96,0:04:40.07,Default,,0000,0000,0000,,we could subtract them first,
Dialogue: 0,0:04:40.07,0:04:41.51,Default,,0000,0000,0000,,we could multiply them.
Dialogue: 0,0:04:41.51,0:04:45.05,Default,,0000,0000,0000,,Many different combinations could give us the same output voltage.
Dialogue: 0,0:04:45.05,0:04:48.16,Default,,0000,0000,0000,,Then here's an example of the way that I chose to do it.
Dialogue: 0,0:04:48.16,0:04:50.81,Default,,0000,0000,0000,,Here is an input resistance, sorry.
Dialogue: 0,0:04:50.81,0:04:58.04,Default,,0000,0000,0000,,Here is an input voltage V1 another input voltage V2, V3, and V4.
Dialogue: 0,0:04:58.04,0:05:02.90,Default,,0000,0000,0000,,I'm going to use a non-inverting amplifier to multiply the first voltage by three,
Dialogue: 0,0:05:02.90,0:05:04.90,Default,,0000,0000,0000,,the second voltage by four,
Dialogue: 0,0:05:04.90,0:05:06.88,Default,,0000,0000,0000,,the third voltage by five,
Dialogue: 0,0:05:06.88,0:05:09.12,Default,,0000,0000,0000,,and the fourth voltage by eight.
Dialogue: 0,0:05:09.12,0:05:13.00,Default,,0000,0000,0000,,I can design a non-inverting amplifier that will do this and I know
Dialogue: 0,0:05:13.00,0:05:17.35,Default,,0000,0000,0000,,that I will be able to do that when I get to the circuit design side of the card.
Dialogue: 0,0:05:17.35,0:05:21.95,Default,,0000,0000,0000,,Well, now that I have multiplied each of my voltages by their appropriate value,
Dialogue: 0,0:05:21.95,0:05:25.16,Default,,0000,0000,0000,,I'm going to take the ones that are positive, right here,
Dialogue: 0,0:05:25.16,0:05:28.96,Default,,0000,0000,0000,,and I'm going to put them into a non-inverting summer and add them up.
Dialogue: 0,0:05:28.96,0:05:32.06,Default,,0000,0000,0000,,So, basically, I'm doing this operation and
Dialogue: 0,0:05:32.06,0:05:35.56,Default,,0000,0000,0000,,here's the output of this non-inverting summer.
Dialogue: 0,0:05:35.56,0:05:37.01,Default,,0000,0000,0000,,On the other side,
Dialogue: 0,0:05:37.01,0:05:39.11,Default,,0000,0000,0000,,I'm going to take the minus five and the minus
Dialogue: 0,0:05:39.11,0:05:41.69,Default,,0000,0000,0000,,eight and put them into an inverting summer.
Dialogue: 0,0:05:41.69,0:05:47.59,Default,,0000,0000,0000,,So, I'm basically doing this part of the math and it's going to show up here.
Dialogue: 0,0:05:47.59,0:05:50.66,Default,,0000,0000,0000,,Finally, I'm simply going to add them up and that gives me
Dialogue: 0,0:05:50.66,0:05:53.76,Default,,0000,0000,0000,,V out on the other side using a non-inverting summer.
Dialogue: 0,0:05:53.76,0:05:57.88,Default,,0000,0000,0000,,So, this is how I use the system design side of my card,
Dialogue: 0,0:05:57.88,0:06:00.48,Default,,0000,0000,0000,,in order to design the operations,
Dialogue: 0,0:06:00.48,0:06:03.46,Default,,0000,0000,0000,,the math, that I want my circuit to do.
Dialogue: 0,0:06:03.46,0:06:08.69,Default,,0000,0000,0000,,Then I flip the cards over to the circuit side and it shows me how to build them.
Dialogue: 0,0:06:08.69,0:06:11.03,Default,,0000,0000,0000,,The non-inverting amplifier of course,
Dialogue: 0,0:06:11.03,0:06:13.82,Default,,0000,0000,0000,,has simply use two resistors and I design them so
Dialogue: 0,0:06:13.82,0:06:16.76,Default,,0000,0000,0000,,that the gain is three, four, five, eight.
Dialogue: 0,0:06:16.76,0:06:19.01,Default,,0000,0000,0000,,Whatever are my gains need to be.
Dialogue: 0,0:06:19.01,0:06:23.80,Default,,0000,0000,0000,,Sorry. Then, I put them into a non-inverting summer,
Dialogue: 0,0:06:23.80,0:06:28.32,Default,,0000,0000,0000,,an inverting summer, and finally a non-inverting summer as shown here.
Dialogue: 0,0:06:28.32,0:06:31.31,Default,,0000,0000,0000,,Now that we know what circuits we're going to do,
Dialogue: 0,0:06:31.31,0:06:33.95,Default,,0000,0000,0000,,let's take a look at the input resistances in
Dialogue: 0,0:06:33.95,0:06:37.62,Default,,0000,0000,0000,,order to decide if we need to put buffers in the circuit.
Dialogue: 0,0:06:37.62,0:06:41.60,Default,,0000,0000,0000,,So, remember that I can design each of these elements independently
Dialogue: 0,0:06:41.60,0:06:45.14,Default,,0000,0000,0000,,as long as the input resistance is near infinity.
Dialogue: 0,0:06:45.14,0:06:48.84,Default,,0000,0000,0000,,Here's my non-inverting summer and sure when I look in here,
Dialogue: 0,0:06:48.84,0:06:51.83,Default,,0000,0000,0000,,Rin is approximately equal to infinity.
Dialogue: 0,0:06:51.83,0:06:55.86,Default,,0000,0000,0000,,So, I do not need buffers on the lines going into this circuit.
Dialogue: 0,0:06:55.86,0:06:59.00,Default,,0000,0000,0000,,When I look at the inverting summer however,
Dialogue: 0,0:06:59.00,0:07:01.25,Default,,0000,0000,0000,,my input resistance is not close to
Dialogue: 0,0:07:01.25,0:07:05.10,Default,,0000,0000,0000,,infinity and so I'm going to need a couple of buffers here.
Dialogue: 0,0:07:05.10,0:07:07.80,Default,,0000,0000,0000,,So, right there I'm going to put a buffer on
Dialogue: 0,0:07:07.80,0:07:11.66,Default,,0000,0000,0000,,either end of the inputs going into my inverting summer.
Dialogue: 0,0:07:11.66,0:07:13.49,Default,,0000,0000,0000,,So, what does that mean?
Dialogue: 0,0:07:13.49,0:07:18.53,Default,,0000,0000,0000,,It means that I can design this card completely separately from this one.
Dialogue: 0,0:07:18.53,0:07:21.59,Default,,0000,0000,0000,,I can design that separately from the non-inverting summer,
Dialogue: 0,0:07:21.59,0:07:24.08,Default,,0000,0000,0000,,separately from the inverting summer and so on,
Dialogue: 0,0:07:24.08,0:07:26.24,Default,,0000,0000,0000,,until I have designed my complete circuit
Dialogue: 0,0:07:26.24,0:07:29.91,Default,,0000,0000,0000,,and then I can hook it up in the fashion shown here.
Dialogue: 0,0:07:30.92,0:07:36.79,Default,,0000,0000,0000,,Sometimes we draw those buffers as black triangles and included that new here as well.
Dialogue: 0,0:07:37.09,0:07:39.98,Default,,0000,0000,0000,,Now, I'd like you to take a chance to read
Dialogue: 0,0:07:39.98,0:07:41.99,Default,,0000,0000,0000,,through example four dash five in your book which is
Dialogue: 0,0:07:41.99,0:07:46.20,Default,,0000,0000,0000,,a practical application of this to the design of an elevation sensor.
Dialogue: 0,0:07:46.20,0:07:49.37,Default,,0000,0000,0000,,I'll let you take the time to work through that example and see if you
Dialogue: 0,0:07:49.37,0:07:53.10,Default,,0000,0000,0000,,understand how the various elements of the system can be put together.
Dialogue: 0,0:07:53.10,0:07:56.98,Default,,0000,0000,0000,,Here's the linear response that your sensor has,
Dialogue: 0,0:07:56.98,0:08:00.80,Default,,0000,0000,0000,,and here's the output that you would like to receive.
Dialogue: 0,0:08:00.80,0:08:03.45,Default,,0000,0000,0000,,See if you can design that circuit.
Dialogue: 0,0:08:03.45,0:08:06.65,Default,,0000,0000,0000,,So, thank you very much for joining me today.
Dialogue: 0,0:08:06.65,0:08:09.89,Default,,0000,0000,0000,,I'm sure you're dying with curiosity about what the front picture was.
Dialogue: 0,0:08:09.89,0:08:11.11,Default,,0000,0000,0000,,This is White Canyon,
Dialogue: 0,0:08:11.11,0:08:14.03,Default,,0000,0000,0000,,a nice ride in American Fork.