Published on April 6, 2014
9/25/2013 1 Topic 6 – Designing Combinational Logic Circuits Faizah Amir EE603 – CMOS IC DESIGN To explain cell design style. To explain dynamic CMOS design. To explain the issues related to pass-transistor design. To explain pass-transistor logic. To explain the properties of complementary CMOS gates. Designing Combinational Logic Circuits Lesson Learning Outcome: 2 3 To construct static CMOS circuit for NAND gate, NOR gate and complex CMOS gate.1 4 5 6
9/25/2013 2 • Difference between combinational logic circuit and sequential logic circuit: Designing Combinational Logic Circuits •Combinational logic (or non-regenerative) circuits : at any point in time, the output of the circuit is related to its current input signals by some Boolean expression. • There is no connection between outputs and inputs is present. •Example: Logic gates, MUX, decoder, adder. •Sequential or regenerative circuits: the output is not only a function of the current input data, but also of previous values of the input signals. •Example circuits are registers, counters, oscillators, and memory. Output = (In)f Output = (In, Previous In)f Static Complementary CMOS • Definition: Static CMOS circuit is a CMOS circuit that its output is connected to either VDD or GND via a low-resistance path, except during switching. • Advantages: i. Robust (low sensitivity to noise – high noise margin) ii. Good performance - low power consumption - high speed
9/25/2013 3 Static Complementary CMOS Pull-up network (PUN) and pull-down network (PDN) PUN and PDN are dual logic networks VDD F(In1,In2,…InN) In1 In2 InN In1 In2 InN PUN PDN PMOS transistors only Pull-up: make a connection from VDD to F when F(In1,In2,…InN) = 1 NMOS transistors only Pull-down: make a connection from F to GND when F(In1,In2,…InN) = 0 Why do we choose PMOS as PUN and NMOS as PDN? The answer is Voltage Drop. Static Complementary CMOS VDD → |VTp| CL S D VGS The output capacitance is initially charged to VDD . PMOS fails to lower the output to zero, but it only reaches the value of |VTp|. NMOS can pass zero without VTn drop. NMOS devices generate “strong zeros”. Pulling down a node using NMOS and PMOS switches VDD → 0 CL VDD S D The output capacitance is initially charged to VDD . NMOS device pulls the output all the way down to GND, without any voltage drop.
9/25/2013 4 Static Complementary CMOS Pulling up a node using NMOS and PMOS switches VDD 0 → VDD CL S D 0 → VDD - VTn CL VDD VDD S D VGS PMOS switch succeeds in charging the output all the way to VDD without any voltage drop. NMOS device fails to raise the output to the value of VDD. The highest value of the output is VDD-VTn. PMOS can pass VDD without VTp drop . PMOS devices generate “strong ones”. Static Complementary CMOS Construction of PDN • NMOS devices in series implement a NAND function • NMOS devices in parallel implement a NOR function
9/25/2013 5 Static Complementary CMOS Construction of PUN • PMOS devices in series implement a NAND function • PMOS devices in parallel implement a NOR function Static Complementary CMOS Dual PUN and PDN • PUN and PDN are dual networks – DeMorgan’s theorems – a parallel connection of transistors in the PUN corresponds to a series connection of the PDN. • Complementary gate is naturally inverting (NAND, NOR). • Number of transistors for an N-input logic gate is 2N.
9/25/2013 6 Static Complementary CMOS Steps to construct CMOS logic circuit: 1. Identify the function f to determine PMOS network. 2. Identify the function f to determine NMOS network. 3. AND function is obtained when the transistors are in series. 4. OR function is obtained when the transistors are in parallel. Static Complementary CMOS How to construct a CMOS logic circuit for 2 input NAND gate? F = A •••• B Steps: 1. F = A + B (PMOS Network) 2. F = A • B (NMOS Network) 3. PMOS are connected in parallel because F is an OR function. 4. NMOS are connected in series because F is an AND function.
9/25/2013 7 Static Complementary CMOS How to construct a CMOS logic circuit for 2 input NOR gate? F = A + B Steps: 1. F = A • B (PMOS Network) 2. F = A + B (NMOS Network) 3. PMOS are connected in series because F is an AND function. 4. NMOS are connected in parallel because F is an OR function. Static Complementary CMOS Complex CMOS Gate Construct a CMOS logic circuit for the Boolean Function below: F = (D + A • (B + C)) VDD PDN PUN VDD STATIC CMOS CIRCUIT
9/25/2013 8 Static Complementary CMOS Stick Diagram : A rough sketch of lines/sticks of different colours showing all the different layers of the design. The diagram is sketched without any rule and can be designed in a short period of time. Static Complementary CMOS • Stick diagram of a complex CMOS logic circuit can be obtained using the method called Euler Path. • Euler-Path Method: 1. Label all the transistor terminals. 2. Determine the shortest path. 3. Transfer all the transistor terminals onto the stick diagram according to the shortest path. 4. Make a connection using metal layer.
9/25/2013 9 Stick Diagram Stick Diagram of 2-input NAND gate: A B F 3 1 3 VDD GND 53 6 2 4 F = A .B 1 2 3 4 2 4 5 6 Draw a Stick Diagram of the complex CMOS circuit below: F = (A + D • (B + C)) Stick Diagram VDD
9/25/2013 10 Solution: Stick Diagram VDD 1 2 3 4 5 6 7 8 4 2 8 6 9 10 PMOS 5 1 1 3 4 2 8 6 3 3 7 7 NMOS 10 9 9 9 4 2 8 6 5 5 10 10 Stick Diagram Stick Diagram for the Boolean Function given: F = (D + A • (B + C)) GND VDD 4 2 8 6 D A B C 5 3 1 7 3 10 5 9 10 9 F X X X X X XX X X
9/25/2013 11 Complementary CMOS Gates a. Noise Margin b. Static Power Consumption c. Propagation delay under appropriate sizing conditions Properties of Complementary CMOS Gates: Complementary CMOS Gates Complementary CMOS gate has high noise margins. It has full rail-to-rail swing with VOH = VDD and VOL = GND a. Noise Margin b. Static Power Consumption Complementary CMOS circuits are designed such that either the pull-down network (PDN) or pull-up network (PUN) is in its ON state at a time. So, no direct path steady state between power and ground and hence, no static power dissipation.
9/25/2013 12 Complementary CMOS Gates Propagation delay is a function of load capacitance and resistance of transistors. Simple RC Model: Delay depending on input patterns VDD VOUT RP CL RP A B B A tPLH ≈ 0.69(RP //RP )CL tPLH ≈ 0.69RPCL tPHL ≈ 0.69(2RN)CL A=0,B=0 A=1,B=1A=0,B=1 Example : 2-input NAND gate c. Propagation Delay Complementary CMOS Gates Static CMOS Gates: Transistor Sizing RPUN ≈ RPDN Inverter 2 input NAND gate 2 input NOR gate According to propagation delay, it is preferred to have tPHL = tPLH, so 1 2 ≅ N P W W
9/25/2013 13 Complementary CMOS Gates Complex CMOS Gates: Sizing Example: Determine the size of each gate for the complementary CMOS circuit below in order to produce the same value of rise and fall times for PUN and PDN. OUT = D + A • (B + C) A B C A D D B C VDD Complementary CMOS Gates Solution: VDD
9/25/2013 14 • A popular and widely-used alternative to complementary CMOS is pass-transistor logic. • Pass-transistor logic reduces the number of transistors required to implement logic. • Pass-transistor logic allows the primary inputs to drive gate terminals as well as source/drain terminals. Pass-Transistor Logic Pass- transistor implementation of AND gate. Pass-Transistor Logic If the B input is high, the top transistor is turned ON and copies the input A to the output F. When B is low, the bottom pass transistor is turned ON and passes a 0. A B F 0 0 0 0 1 0 1 0 0 1 1 1 F = A•B
9/25/2013 15 • For high performance design, a differential pass-transistor logic family, called CPL or DPL is commonly used. Differential Pass- transistor Logic Basic Concept of Differential Pass-transistor Logic Example differential pass-transistor networks: a) AND/NAND Gate Differential Pass- transistor Logic AND Gate: NAND Gate: A B F 0 0 0 0 1 0 1 0 0 1 1 1 A B F 0 0 1 0 1 1 1 0 1 1 1 0 F = A •B F = A •B F = A •B
9/25/2013 16 b) OR/NOR Gate Differential Pass- transistor Logic OR Gate: A B F 0 0 0 0 1 1 1 0 1 1 1 1 NOR Gate: A B F 0 0 1 0 1 0 1 0 0 1 1 0 F = A + B F = A + B F = A + B c) XOR/XNOR Gate Differential Pass- transistor Logic XOR Gate: A B F 0 0 0 0 1 1 1 0 1 1 1 0 XNOR Gate: A B F 0 0 1 0 1 0 1 0 0 1 1 1 F = AB +A B = A ⊕ B = A ⊕ B F = AB +A B So, F = A ⊕ B
9/25/2013 17 Advantage of pass-transistor design: - Fast and simple design - Complex gates can be implemented using minimum number of transistors, which also reduces parasitics. Disadvantages of pass-transistor design: - Reduces the noise margin due to the threshold voltage drop - Increases static power dissipation So, how do we overcome the disadvantages? Pass-Transistor Logic Solutions to deal with the problems in pass- transistor logic: a. Level restoration b. Multiple-threshold transistor c. Transmission-gate logic Pass-Transistor Logic
9/25/2013 18 a. Level restoration A single PMOS configured in a feedback path. The gate of the PMOS device is connected to the output of the inverter, its drain connected to the input of the inverter and the source to VDD. Pass-Transistor Logic If X is at 0V, Out is at VDD and the Mr is turned OFF with B = VDD and A = 0. If input A makes a 0 to VDD transition, Mn only charges up node X to VDD-VTn. This voltage is enough to switch the output of the inverter low, turning ON the feedback device Mr and pulling node X all the way to VDD. No static power dissipation in the inverter. Also, no static current path can exist through the level restorer and the pass-transistor, since the restorer is only active when A is high. So, no static power is consumed. b. Multiple-threshold transistor Voltage-drop problem associated with pass-transistor logic can be solved by using multiple-threshold devices. Using zero threshold devices for the NMOS pass-transistors eliminates most of the threshold drop, and passes a signal close to VDD. However, the use of zero-threshold transistors can be dangerous due to the sub-threshold currents that can flow through the pass- transistors, even if VGS is slightly below VT. Pass-Transistor Logic Static power consumption when using zero-threshold pass-transistors.
9/25/2013 19 c. Transmission-gate logic • The most widely-used solution to deal with the voltage-drop problem is the use of transmission gates. •It builds on the complementary properties of NMOS and PMOS transistors: NMOS devices pass a strong 0 but a weak 1, while PMOS transistors pass a strong 1 but a weak 0. Pass-Transistor Logic The control signals of the transmission gate are C and its complementary C. If C = 0, both transistors are OFF, creating an open circuit between nodes A and B. When C = 1: if A=1, PMOS will pass ‘1’ to B. if A=0, NMOS will pass ‘0’ to B. • In static circuits at every point in time (except when switching) the output is connected to either GND or VDD via a low resistance path. » fan-in of N requires 2N devices • Dynamic circuits rely on the temporary storage of signal values on the capacitance of high impedance nodes. » requires on N + 2 transistors Dynamic CMOS Logic
9/25/2013 20 There are two phase of operation: • Pre-charge phase – When the clock is low, the PMOS (Mp) is ON and the NMOS (Me) is OFF. So the capacitor at the output gets charged to VDD, thus changing to logic 1. • Evaluate phase – When the clock is high, Mp is OFF and Me is ON. The output capacitance gets discharged conditionally based on the logic function implemented by PDN, thus changing to logic 0. Dynamic CMOS Logic • Example Dynamic CMOS Logic PDN During the precharge phase: CLK=0 The output is precharged to VDD regardless of the input values. During evaluation phase: CLK=1 A conducting path is created between Out and GND if (and only if) A•B+C is TRUE. Otherwise, the output remains at the precharged state of VDD. The function for output: Out = CLK + (A•B + C) • CLK
9/25/2013 21 Speed and power dissipation of dynamic logic: • Dynamic logic only consumes dynamic power. Ideally, no static current path ever exists between VDD and GND. The overall power dissipation, however, can be significantly higher compared to a static logic gate. • The dynamic logic gates have faster switching speeds. There are two main reasons for this: i. Because of the reduced load capacitance attributed to the lower number of transistors per gate and the single-transistor load per fan-in. ii. The dynamic gate does not have short circuit current, and all the current provided by the pull-down devices goes towards discharging the load capacitance. Dynamic CMOS Logic Issues in dynamic CMOS design: a. Charge leakage b. Charge sharing c. Capacitive coupling d. Clock-feed through Dynamic CMOS Logic
9/25/2013 22 a. Charge leakage • The operation of a dynamic gate relies on the dynamic storage of the output value on a capacitor. If the pull-down network is off, the output should ideally remain at the precharged state of VDD during the evaluation phase. • However, this charge gradually leaks away due to leakage currents, eventually resulting in a malfunctioning of the gate. Dynamic CMOS Logic Sets the minimum clock to 250Hz to 1kHz. b. Charge sharing • Charge stored originally on CL is redistributed (shared) over CL and CA leading to static power consumption by the gates in PDN and can cause circuit malfunction. Dynamic CMOS Logic During the precharge phase, the output node is precharged to VDD. Assume that all inputs are set to ‘0‘ during precharge, and that the capacitance CA is discharged. Assume further that input B remains at ‘0’ during evaluation, while input A makes a ‘0’ ‘1’ transition, turning transistor Ma ON. The charge stored originally on capacitor CL is redistributed over CL and CA. This causes a drop in the output voltage, which cannot be recovered due to the dynamic nature of the circuit. VDD Ma
9/25/2013 23 c. Capactive/Backgate coupling • The high impedance of the output node makes the circuit very sensitive to crosstalk effects. A wire routed over a dynamic node may couple capacitively and destroy the state of the floating node. Example : A dynamic two-input NAND gate drives a static NAND gate. Dynamic CMOS Logic A transition in the input (In) may cause the output of dynamic gate Out1 to drop due to capacitive coupling. This may cause Out2 not to drop all the way to ‘0’ and could cause static power to be dissipated. If the voltage drop is large enough, the circuit can evaluate incorrectly. VDD VDD d. Clock-feed through • Clock-feed through is an effect caused by the capacitive coupling between the clock input of the precharge device and the dynamic output node. Dynamic CMOS Logic VDD Coupling between Out and CLK input of the precharge device is due to the gate to drain capacitance. So, voltage Out can rise above VDD. The fast rising (and falling edges) of the clock couple to Out.
9/25/2013 24 Cell-based design style use a standard cell library as the basic building blocks of a chip. • Cell-based design advantages: – Smaller, faster, and lower-power chips. – Reduce design cost because the cost for custom mask set needs high NRE only economical for high volume parts. – Much higher productivity. • CMOS Cell design style: a. Standard cells b. Data paths cells Cell-Based Design Style a. Standard cell • Standard cell design involves the use of pre-designed standard cell @ library cell that has been and stored in database. • Standard cell @ library cell consists of simple circuit such as inverter or logic gates (AND, OR, XOR, XNOR, flip-flop), and complex circuit such as register, adder, ROM and RAM. • Design is carried out by simply using the pre-designed cells from the library and then connect the cells so that certain functions can be implemented. • To facilitate placement and routing, the standard cells are designed to have equal height but variable widths, so that the final IC layout will have a regular pattern with rows of cells and interconnect routing running between the rows. Cell-Based Design Style
9/25/2013 25 Standard Cell Functional module (RAM, multiplier, …) Routing channel Logic cellFeedthrough cell Rowsofcells Standard Cell Layout Standard Cell : very popular due to high degree of automation Standard Cell Standard Cell Example
9/25/2013 26 b. Data paths cell In data paths cell style, the main power and control signals, and the parallel bus carrying data are normally drawn vertically in parallel line with a pitch adjusted to accommodate the layout of all the required circuitry under the main stream of metals containing the important signals. • Wires over cells - Horizontal wires carry data between function units, busses in the design. - Vertical wires are the control lines for the function. Cell-Based Design Style Example of Data path Cell Design Style: Data Paths Cell Style Data path: Wires are in the Cell.
9/25/2013 27 1. Static complementary CMOS combines dual pull-down and pull-up networks, only one of which is enabled at any time. 2. CMOS gate has good performance with low power consumption, high noise margin and its propagation delay is a strong function of the fan-in. Technique to deal with fan-in include transistor sizing. 3. NMOS-only pass-transistor logic implements a logic gate as a simple switch network that produces simple structure to implement some logic functions. 4. Pass-transistor logic suffers from static power consumption and reduced noise margins. This problem can be addressed by adding a level-restoring transistor. 5. The operation of dynamic logic is based on the storage of charge on a capacitive node and the conditional discharging of that node as a function of the inputs. The operation has two-phase scheme, consisting of a precharge followed by an evaluation step. The circuit is less complex and operate faster, however, it is prone to fail due to increased sensitivity to noise 6. Standard Cell is a general purpose logic that is based on predesigned library cell and Datapath Cell includes some wiring in the cell. Summary 1. Construct a static Complementary CMOS circuit for the function below: (4 marks) 2. Based on the static complementary CMOS circuit below: a. Determine the Boolean function for F. (2 marks) b. Produce a stick diagram for the circuit. (5 marks) Past Year Questions )()( ACDBF •+•= VDD A B C D B C F A D
9/25/2013 28 3. Given that (W/L)p = (1.2µm/0.25µm) and (W/L)n = (0.6µm/0.25µm) Determine the appropriate size of the transistors for the circuits below: Past Year Questions A D A B VDD F=A.B.C B C C D F=(AB)+ C A C B BA C VDD a. b. Designing Combinational Logic Circuits
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