nldm (non-linear delay model)
**NLDM (Non-Linear Delay Model)** is the foundational **table-based timing model** used in Liberty (.lib) files — representing cell delay and output transition time as **2D lookup tables** indexed by input slew and output capacitive load, capturing the non-linear relationship between these variables and delay.
**Why "Non-Linear"?**
- Simple linear delay models (e.g., $d = R \cdot C_{load}$) assume delay is proportional to load — this is only approximately true.
- Real cell delay vs. load relationship is **non-linear**: at low loads, internal delays dominate; at high loads, the driving resistance matters more.
- Similarly, delay depends non-linearly on input slew — a slow input causes more short-circuit current and affects switching dynamics.
- NLDM captures this non-linearity through **table interpolation** rather than equations.
**NLDM Table Structure**
- Two tables per timing arc:
- **Cell Delay Table**: delay = f(input_slew, output_load)
- **Output Transition Table**: output_slew = f(input_slew, output_load)
- Each table is typically **5×5 to 7×7** entries:
- **Rows (index_1)**: Input slew values (e.g., 5 ps, 10 ps, 20 ps, 50 ps, 100 ps, 200 ps, 500 ps)
- **Columns (index_2)**: Output load values (e.g., 0.5 fF, 1 fF, 2 fF, 5 fF, 10 fF, 20 fF, 50 fF)
- **Entries**: Delay or transition time in nanoseconds
- During timing analysis, the tool **interpolates** (or extrapolates) between table entries to get the delay for the actual slew and load values.
**NLDM Delay Calculation Flow**
1. The STA tool knows the input slew (from the driving cell's output transition table).
2. The STA tool knows the output load (sum of wire capacitance + downstream pin capacitances).
3. Look up the cell delay table → get propagation delay.
4. Look up the output transition table → get output slew.
5. Pass the output slew to the next cell in the path.
6. Repeat through the entire timing path.
**NLDM Limitations**
- **Output Modeled as Ramp**: NLDM represents the output waveform as a simple linear ramp (characterized by a single slew value). Real waveforms are non-linear.
- **No Waveform Shape**: At advanced nodes, the actual shape of the voltage waveform matters for delay, noise, and SI analysis — NLDM doesn't capture this.
- **Load Independence**: NLDM assumes the output waveform shape is independent of the downstream network's response — actually, the load network affects the waveform.
- **Miller Effect**: The non-linear interaction between input and output transitions (Miller capacitance) is not fully captured.
**When NLDM Is Sufficient**
- At **45 nm and above**: NLDM is generally accurate enough for most digital timing.
- At **28 nm and below**: CCS or ECSM provides better accuracy, especially for setup/hold analysis and noise.
- **Most digital logic**: NLDM remains widely used for standard timing analysis even at advanced nodes, with CCS/ECSM used for critical paths.
NLDM is the **workhorse timing model** of digital design — simple, fast, and accurate enough for the vast majority of timing analysis scenarios.