Signaling: Analog: each processing step accumulates noise Digital: each processing step restores output to a valid digital level Needed: Noise Margins! A Digital Processing Element A combinational device is a circuit element that has: one or more digital inputs one or more digital outputs a functional specification relating the value of each output to every possible combination of valid input values VALID INPUT REPRESENTATIONS VALID OUTPUT REPRESENTATIONS A combinational device accepts marginal inputs and provides unquestionable outputs (to leave room for noise). A Combinational Digital System A set of interconnected elements is a combinational device if: each circuit element is combinational every input is connected to exactly one output or to some vast supply of constant 0's and 1's the circuit contains no directed cycles Why is this true? Voltage Transfer Characteristic Note the VTC can do anything when V_in is between V_IL and V_IH. Note that the center white region is taller than it is wide (V_OH - V_OL > V_IH - V_IL). Net result, combinational devices can be NONLINEAR. Problem 1: Ms. Anna Logge, founder at a local MIT start-up, has developed a device to be used as an inverter. Anna is considering the choice of parameters by which her logic family will represent logic values and needs your help. The voltage transfer curve of a proposed inverter for a new logic family is shown to the right (spare copies of this diagram can be found below). Several possible schemes for mapping logic values to voltages are being considered, as summarized in the incomplete table below. Recall that Noise Immunity (last row) is defined as the lesser of the two noise margins. Complete the table by filling in missing entries. Choose each value you enter so as to maximize the noise margins of the corresponding scheme. If the numbers in a scheme can't be completed such that the device functions as an inverter with positive noise margins, put an X in the entries for that column. LNI's Possible Logic Mappings: Scheme Vol Vil Vih Voh Noise Immunity A X X B 0.5 C 1 Problem 2: The following are voltage transfer characteristics of single-input, single-output devices to be used in a new logic family: Device A [Insert voltage transfer curve for Device A] Device B [Insert voltage transfer curve for Device B] Your job is to choose a single set of signaling thresholds (V_{IL}), (V_{IH}), (V_{OL}), and (V_{OH}) to be used with both devices to give the best noise margins you can. Recall that the VTC can touch the edge of the forbidden regions but not pass through those regions. Fill in your answers below, together with the resulting noise margins. You'll get partial credit for anything that works with nonzero noise margins; for full credit, maximize the noise immunity (i.e., the smaller of the two noise margins). | | | | | | |---|---|---|---|---| | (V_{IL}) = | 0.5 | | | | | (V_{IH}) = | 1.5 | | | | | (V_{OL}) = | | | | | | (V_{OH}) = | | | | | | Low Noise Margin = | | | | | | High Noise Margin = | | | | | Additional notes: Also, (V_{IL}) ≤ 1.667 Works if (V_{OH}) ≥ 4.5 But noise margin = 1.667 - 0.5 = 1.167 But noise immunity unchanged!