1 00:00:00,650 --> 00:00:05,320 Let's make some measurements using one of the simplest combinational devices: a buffer. 2 00:00:05,320 --> 00:00:10,469 A buffer has a single input and a single output, where the output will be driven with the same 3 00:00:10,469 --> 00:00:15,659 digital value as the input after some small propagation delay. 4 00:00:15,659 --> 00:00:20,580 This buffer obeys the static discipline - that's what it means to be combinational - and uses 5 00:00:20,580 --> 00:00:27,130 our revised signaling specification that includes both low and high noise margins. 6 00:00:27,130 --> 00:00:31,470 The measurements will be made by setting the input voltage to a sequence of values ranging 7 00:00:31,470 --> 00:00:35,450 from 0V up to the power supply voltage. 8 00:00:35,450 --> 00:00:39,590 After setting the input voltage to a particular value, we'll wait for the output voltage to 9 00:00:39,590 --> 00:00:45,540 become stable, i.e., we'll wait for the propagation delay of the buffer. 10 00:00:45,540 --> 00:00:49,930 We'll plot the result on a graph with the input voltage on the horizontal axis and the 11 00:00:49,930 --> 00:00:53,580 measured output voltage on the vertical axis. 12 00:00:53,580 --> 00:00:59,080 The resulting curve is called the voltage transfer characteristic of the buffer. 13 00:00:59,080 --> 00:01:05,019 For convenience, we've marked our signal thresholds on the two axes. 14 00:01:05,019 --> 00:01:09,050 Before we start plotting points, note that the static discipline constrains what the 15 00:01:09,050 --> 00:01:14,140 voltage transfer characteristic must look like for any combinational device. 16 00:01:14,140 --> 00:01:18,850 If we wait for the propagation delay of the device, the measured output voltage must be 17 00:01:18,850 --> 00:01:24,890 a valid digital value if the input voltage is a valid digital value - "valid in, valid 18 00:01:24,890 --> 00:01:27,470 out". 19 00:01:27,470 --> 00:01:32,600 We can show this graphically as shaded forbidden regions on our graph. 20 00:01:32,600 --> 00:01:37,620 Points in these regions correspond to valid digital input voltages but invalid digital 21 00:01:37,620 --> 00:01:39,660 output voltages. 22 00:01:39,660 --> 00:01:43,970 So if we're measuring a legal combinational device, none of the points in its voltage 23 00:01:43,970 --> 00:01:46,940 transfer characteristic will fall within these regions. 24 00:01:46,940 --> 00:01:53,440 Okay, back to our buffer: setting the input voltage to a value less than the low input 25 00:01:53,440 --> 00:01:58,020 threshold V_IL, produces an output voltage less than V_OL, as expected. 26 00:01:58,020 --> 00:02:05,170 A digital 0 input yields a digital 0 output. 27 00:02:05,170 --> 00:02:10,649 Trying a slightly higher but still valid 0 input gives a similar result. 28 00:02:10,649 --> 00:02:14,530 Note that these measurements don't tell us anything about the speed of the buffer, they 29 00:02:14,530 --> 00:02:20,519 are just measuring the static behavior of the device, not its dynamic behavior. 30 00:02:20,519 --> 00:02:24,900 If we proceed to make all the additional measurements, we get the voltage transfer characteristic 31 00:02:24,900 --> 00:02:29,560 of the buffer, shown as the black curve on the graph. 32 00:02:29,560 --> 00:02:34,099 Notice that the curve does not pass through the shaded regions, meeting the expectations 33 00:02:34,099 --> 00:02:39,418 we set out above for the behavior of a legal combinational device. 34 00:02:39,418 --> 00:02:43,810 There are two interesting observations to be made about voltage transfer characteristics. 35 00:02:43,810 --> 00:02:48,730 Let's look more carefully at the white region in the center of the graph, corresponding 36 00:02:48,730 --> 00:02:53,200 to input voltages in the range V_IL to V_IH. 37 00:02:53,200 --> 00:02:58,189 First note that these input voltages are in the forbidden zone of our signaling specification 38 00:02:58,189 --> 00:03:03,069 and so a combinational device can produce any output voltage it likes and still obey 39 00:03:03,069 --> 00:03:09,349 the static discipline, which only constrains the device's behavior for *valid* inputs. 40 00:03:09,349 --> 00:03:14,219 Second, note that the center white region bounded by the four voltage thresholds is 41 00:03:14,219 --> 00:03:16,480 taller than it is wide. 42 00:03:16,480 --> 00:03:22,719 This is true because our signaling specification has positive noise margins, so V_OH - V_OL 43 00:03:22,719 --> 00:03:27,209 is strictly greater than V_IH - V_IL. 44 00:03:27,209 --> 00:03:31,920 Any curve passing through this region - as the VTC must - has to have some portion where 45 00:03:31,920 --> 00:03:36,129 the magnitude of the slope of the curve is greater than 1. 46 00:03:36,129 --> 00:03:40,230 At the point where the magnitude of the slope of the VTC is greater than one, note that 47 00:03:40,230 --> 00:03:46,249 a small change in the input voltage produces a larger change in the output voltage. 48 00:03:46,249 --> 00:03:50,269 That's what it means when the magnitude of the slope is greater than 1. 49 00:03:50,269 --> 00:03:55,560 In electrical terms, we would say the device as a gain greater than 1 or less than -1, 50 00:03:55,560 --> 00:04:02,219 where we define gain as the change in output voltage for a given change in input voltage. 51 00:04:02,219 --> 00:04:07,280 If we're considering building larger circuits out of our combinational components, any output 52 00:04:07,280 --> 00:04:10,709 can potentially be wired to some other input. 53 00:04:10,709 --> 00:04:16,529 This means the range on the horizontal axis (V_IN) has to be the same as the range on 54 00:04:16,529 --> 00:04:24,139 the vertical axis (V_OUT), i.e., the graph of VTC must be square and the VTC curve fits 55 00:04:24,139 --> 00:04:27,000 inside the square. 56 00:04:27,000 --> 00:04:31,680 In order to fit within the square bounds, the VTC must change slope at some point since 57 00:04:31,680 --> 00:04:36,020 we know from above there must be regions where the magnitude of the slope is greater than 58 00:04:36,020 --> 00:04:41,240 1 and it can't be greater than 1 across the whole input range. 59 00:04:41,240 --> 00:04:46,300 Devices that exhibit a change in gain across their operating range are called nonlinear 60 00:04:46,300 --> 00:04:48,770 devices. 61 00:04:48,770 --> 00:04:54,090 Together these observations tell us that we cannot only use linear devices such as resistors, 62 00:04:54,090 --> 00:04:57,560 capacitors and inductors, to build combinational devices. 63 00:04:57,560 --> 00:05:02,090 We'll need nonlinear devices with gain greater than 1. 64 00:05:02,090 --> 00:05:05,180 Finding such devices is the subject of the next chapter.