Quiz: Modeling skew requirements with data-to-data setup and hold checks

Problem: Suppose there are 'N' signals which are to be skew matched within a window of 200 ps with respect to each other. Model this requirement with the help of data setup and hold checks.

As we discussed in data setup and data hold checks, data setup check of 200 ps means that constrained data should come at least 200 ps before the reference data. Similarly, data hold check of 200 ps constrains the constrained data to come at least 200 ps after the reference data. The same is shown pictorially in figure 1(a) and 1(b).

Figure 1(a): Data setup check of 200 ps constrains the constrained signal to toggle at-least 200 ps before reference signal toggles.

Figure 1(b): Data hold check of 200 ps constrains the constrained signal to toggle at-least 200 ps after the reference signal has toggled.

Now, suppose you apply a data setup check of -200 ps instead of 200 ps. This would mean that the constrained signal can toggle upto 200 ps after the reference signal. Similarly, a data hold check of -200 ps would mean that the constrained signal can toggle from 200 ps before the reference signal. If we apply both the checks together, it would infer that constrained signal can toggle in a window that ranges from 200 ps before the toggling of reference signal to 200 ps after the toggling of reference signal. This is pictorially shown in figures 2(a) and 2(b).

Figure 2(a): Negative data setup and hold checks of 200 ps

If we combine the two checks, it implies that the constrained data can toggle upto 200 ps after and from 200 ps before the reference signal. In other words, we have constrained the constrained signal to toggle in a window +- 200 ps within the reference signal.

Coming to the given problem, if there are a number of signals required to toggle within a window of 200 ps, we can consider one of these to act as reference signal and other signals as constrained signals. The other signals can then be constrained in both setup and hold with respect to reference signal such that all of these lie within +-100 ps of the reference signal. The same is shown in figure 3 below:

Figure 3: Data checks to maintain skew between N signals

Lockup latches vs. lockup registers: what to choose

Both lockup latches and lockup registers are used to make scan chain robust to hold failures. What one uses for the same depends upon his/her priorities and the situation. However, it seems lockup latches are more prevalent in designs of today. This might be due to following reasons:

1. Area: As we know, a latch occupies only half the area as a register. So, using lockup latches instead of lockup registers gives us area and power advantage; i.e., less overhead.
2. Timing: Lockup elements – timing perspective has given an analysis of how timing critical lockup elements (lockup latches and lockup registers) paths can be. According to it, using a negative lockup latch, you don’t have to meet timing at functional (at-speed) frequency. However, in all other cases, you need to meet timing. This might also be a reason people prefer lockup latches.

Lockup latches, on one hand relax only one side hold. So, you can afford to have skew only on one side, either on launch or on capture. Lockup registers, on the other hand, let you have skew on both the sides. So, lockup latches are preferable where you can afford to have tap on the clock either from launch flop or on capture flop. On the other hand, lockup flops can be used by tapping clock from any point as long as you meet setup and hold timings.

Hope you’ve found this post useful. Let us know what you think in the comments.

Time borrowing in latches

What is time borrowing: Latches exhibit the property of being transparent when clock is asserted to a required value. In sequential designs, using latches can enhance performace of the design. This is possible due to time borrowing property of latches. We can define time borrowing in latches as follows:

Time borrowing is the property of a latch by virtue of which a path ending at a latch can borrow time from the next path in pipeline such that the overall time of the two paths remains the same. The time borrowed by the latch from next stage in pipeline is, then, subtracted from the next path's time.

The time borrowing property of latches is due to the fact that latches are level sensitive; hence, they can capture data over a range of times than at a single time, the entire duration of time over which they are transparent. If they capture data when they are transparent, the same point of time can launch the data for the next stage (of course, there is combinational delay from data pin of latch to output pin of latch).

Let us consider an example wherein a negative latch is placed between two positive edge-triggered registers for simplicity and ease of understanding. The schematic diagram for the same is shown in figure 1 below:

Figure 1: Negative level-sensitive latch between two positive edge-triggered registers

Figure 2 below shows the clock waveform for all the three elements involved. We have labeled the clock edges for convenience. As is shown, latB is transparent during low phase of the clock. RegA and RegC (positive edge-triggered registers) can capture/launch data only at positive edge of clock; i.e., at Edge1, Edge3 or Edge5. LatB, on other hand, can capture and launch data at any instant of time between Edge2 and Edge3 or Edge4 and Edge5.

Figure 2: Clock waveforms

The time instant at which data is launched from LatB depends upon the time at which data launched from RegA has become stable at the input of latB. If the data launched at Edge1 from RegA gets stable before Edge2, it will get captured at Edge2 itself.  However, if the data is not able to get stable, even then, it will get captured. This time, as soon as the data gets stable, it will get captured. The latest instant of time this can happen is the latch closing edge (Edge3 here). One point here to be noted is that at whatever point data launches from LatB, it has to get captured at RegC at edge3. The more time latch takes to capture the data, it gets subtracted from the next path. The worst case setup check at latB is at edge2. However, latch can borrow time as needed. The maximum time borrowed, ideally, can be upto Edge3. Figure 3 below shows the setup and hold checks with and without time borrow for this case:

Figure 3: Setup check with and without time borrow

The above example consisted of a negative level-sensitive latch. Similarly, a positive level-sensitive latch will also borrow time from the next stage, just the polarities will be different.

Also read:

• Metastability
• Lockup latch - principle, application and timing
• Setup check and hold check for register to latch timing paths
• False paths - basics and example scenarios
• Can hold be frequency dependent

2-input gates using 2:1 mux

Definition of a multiplexer: A 2^n-input mux has n select lines. It can be used to implement logic functions by implementing LUT (Look-Up Table) for that function. A 2-input mux can implement any 2-input function, a 4-input mux can implement any 3-input, an 8-input mux can implement any 4-input function, and so on. This property of muxes makes FPGAs implement programmable hardware with the help of LUT muxes. In this post, we will be discussing the implementation of 2-input AND, OR, NAND, NOR, XOR and XNOR gates using a 2-input mux.

2-input AND gate implementation using 2:1 mux: Figure 1 below shows the truth table of a 2-input AND gate. If we observe carefully, OUT equals '0' when A is '0'. And OUT follows B when A is '1'. So, if we connect A to the select pin of a 2:1 mux, AND gate will be implemented if we connect D0 to '0' and D1 to 'B'.

Figure 1: Truth table of AND gate

Figure 2 below shows the implementation of 2-input AND gate using a 2:1 multiplexer.

Figure 2: Implementation of AND gate using a 2:1 mux

2-input NAND gate using 2:1 mux: Figure 3 below shows the truth table of a 2-input NAND gate. If we observe carefully, OUT equals '1' when A is '0'. Similarly, when A is '1', OUT is B'. So, if we connect SEL pin of mux to A, D0 pin of mux to '1' and D1 to B', then it will act as a NAND gate.

Figure 3: Truth table of 2-input NAND gate

Figure 4 below shows the implementation of a 2-input NAND gate using 2:1 mux.

Figure 4: Implementation of 2-input NAND gate using 2:1 mux

2-input OR gate using 2x1 mux: Figure 5 below shows the truth table for a 2-input OR gate. If we observe carefully, OUT equals B when A is '0'. Similarly, OUT is '1' (or A), when A is '1'. So, we can make a 2:1 mux act like a 2-input OR gate, if we connect D0 pin to B and D1 pin to A, with select connected to A.

Figure 5: Truth table of 2-input OR gate

Figure 6 below shows the implementation of 2-input OR gate using a 2:1 multilpexer:

Figure 6: Implementation of 2-input OR gate using 2:1 mux

2-input NOR gate using 2x1 mux: Figure 7 below shows the truth table of a 2-input NOR gate. If we observe carefully, OUT equal B' when A is '0'. Similarly, OUT equals '0' when A is '1'. So, we can make a 2-input mux act like a 2-input NOR gate, if we connect SEL of mux to A, D0 to B' and D1 to '0'.

Figure 7: Truth table of 2-input NOR gate

Figure 8 shows the implementation of 2-input NOR gate using 2:1 mux.

Figure 8: Implementation of 2-input NOR gate using 2x1 mux

2-input XNOR gate using 2x1 mux: Figure 9 below shows the truth table of a 2-input XNOR gate. If we observe carefully, OUT equals B' when A is '0' and equals B when A is '1'. So, a 2-input XNOR gate can be implemented from a 2x1 mux, if we connect SEL pin to A, D0 to B' and D1 to B.

Figure 9: Truth table of 2-input XNOR gate

The implementation of 2-input XOR gate using a 2x1 mux is as shown in figure 10.

Figure 10: Implementation of 2-input XNOR gate using 2x1 mux

2-input XOR gate using 2x1 mux: Figure 11 shows the truth table for a 2-input XOR gate. If we observe carefully, OUT equals B when A is '0' and B' when A is '1'. So, a 2:1 mux can be used to implement 2-input XOR gate if we connect SEL to A, D0 to B and D1 to B'.

Figure 11: Truth table of 2-input XOR gate

Figure 12 shows the implementation of 2-input XOR gate using 2x1 mux.

Implementation of 2-input XOR gate using 2x1 mux

NOT gate using 2:1 mux: Figure 13 shows the truth table for a NOT gate. The only inverting path in a multiplexer is from select to output. To implement NOT gate with the help of a mux, we just need to enable this inverting path. This will happen if we connect D0 to '1' and D1 to '0'.

Figure 13: Truth table of NOT gate

Figure 14 shows the implementation of NOT gate using 2x1 mux:

Figure 14: Implementation of NOT gate using 2x1 mux