Artificial Intelligence Response
Direct answer to the question
- I can design a folded-cascode operational amplifier for you, but I need your exact specs to size devices and set the bias network precisely.
- If you don’t have all specs yet, use the template below. I also include a complete, worked first‑pass design example you can adapt.
Key points
- Please provide: supply (VDD/VSS), DC gain, UGB/GBW, phase margin, load C and R, slew rate, input CM range, output swing, power budget, technology node and models.
- Below you’ll find: a robust, step‑by‑step sizing method (gm/ID based), headroom checks, stability/compensation strategy, CMFB (for fully differential), noise/mismatch guidance, and a verification plan.
Detailed problem analysis
1) Topology choice and operating point
- Use a single‑stage NMOS input folded cascode (FC) for high gain and wide input CM range at low VDD. Choose single‑ended output (no CMFB needed) or fully differential (requires CMFB).
- Design targets couple tightly: for a one‑stage FC driving CL, the unity gain bandwidth is set by the input pair transconductance: UGB ≈ gm1/(2πCL). Slew rate is set by the max output current into CL.
2) Primary equations and design flow (works for any node/PDK)
- Unity‑gain bandwidth:
\[ \mathrm{UGB} \approx \frac{g_{m1}}{2\pi CL} \Rightarrow g{m1} = 2\pi\, C_L\, \mathrm{UGB}. \]
- Slew rate (conservative for single‑ended FC; m is any mirror gain at the output, usually 1):
\[ \mathrm{SR} \approx \frac{I_{out,\max}}{CL} \approx \frac{m\,I{\text{branch}}}{C_L}. \]
A safe rule is Itail ≥ SR·CL for at least one polarity; for symmetric slewing ensure both sourcing and sinking paths can deliver SR·CL.
- gm/ID method (recommended over square‑law at deep sub‑µm):
\[ I_{D} = \frac{g_m}{(g_m/ID)}, \quad V{ov} \approx \frac{2I_D}{g_m}. \]
Choose gm/ID per device role:
- Input pair: 12–18 V⁻¹ (speed/noise balance).
- Folded devices and output devices: 8–14 V⁻¹ (headroom and high gm).
- Cascodes: 6–10 V⁻¹ (small Vov to preserve swing, long L to boost ro).
- DC gain of a folded cascode (single‑ended) roughly:
\[ A0 \approx g{m1}\, R{out}, \quad R{out} \approx \left(r{o,n}(1+g{m,cn}r{o,cn})\right) \parallel \left(r{o,p}(1+g{m,cp}r{o,cp})\right). \]
Long‑L cascodes with decent gm·ro (>50–150) can yield Rout in tens of MΩ, enabling 80 dB+.
- Headroom (VDD referenced high side, VSS referenced low side). With small overdrives:
- Vout,max ≈ VDD − (Vov,Pout + Vov,Pcas)
- Vout,min ≈ VSS + (Vov,Nout + Vov,Ncas)
Keep each Vov ≈ 120–180 mV to get large swing on 1.2–1.8 V supplies.
- Dominant pole and non‑dominant poles:
- p0 ≈ 1/(Rout·(CL + Cout_parasitic)).
- Non‑dominant poles at folded nodes and cascode nodes; push them above UGB by keeping parasitics low (narrow W for cascodes) and gm of cascodes reasonably high.
3) Worked first‑pass example (you can replace numbers with your specs)
Assume:
- Process: generic CMOS (e.g., 180 nm), models available.
- VDD = 1.8 V, VSS = 0 V.
- CL = 2 pF.
- UGB = 50 MHz.
- PM ≥ 60°.
- SR ≥ 20 V/µs.
- Target A0 ≥ 80 dB (10,000 V/V).
- Power ≤ 1 mW.
- NMOS input pair, single‑ended output.
Step A: Set gm from UGB
- gm1 = 2π·CL·UGB = 2π·(2 pF)·(50 MHz) ≈ 0.628 mS.
Step B: Tail current from gm/ID
- Choose (gm/ID)in ≈ 15 V⁻¹ → Id,per‑input = gm1/(gm/ID) ≈ 0.628 mS / 15 ≈ 41.9 µA.
- Itail ≈ 2·Id ≈ 84 µA.
Step C: Check slew requirement
- SR·CL = 20 V/µs · 2 pF = 40 µA. The output path must source/sink ≥ 40 µA. Set each folded branch current Ifold ≈ 70–80 µA to allow both polarities with margin.
Step D: Choose overdrives and lengths
- Aim Vov ≈ 0.13–0.18 V for all stacked devices.
- Use long L for cascodes (e.g., Lcasc ≈ 1.0–1.5 µm in a 180 nm PDK) to boost ro; use moderate L for input pair (≥ 0.5–1.0 µm for flicker noise/ro).
- For area/parasitics, keep cascodes narrow while meeting Vov at the chosen current.
Step E: Rough gain feasibility
- With long‑L cascodes, gm_casc ≈ Id/Vov ≈ 80 µA / 0.15 V ≈ 0.53 mS.
- If each device ro ≈ 200–400 kΩ at these L and currents, then gm·ro of cascodes ≈ 100–200 → per‑side boosted ro in tens of MΩ. Two sides in parallel still leaves Rout ~15–25 MΩ.
- A0 ≈ gm1·Rout ≈ 0.628 mS · (16–25 MΩ) ≈ 10,000–15,700 V/V → 80–84 dB. If short, increase L of cascodes or add gain‑boosting (see below).
Step F: Stability/compensation
- One‑stage FC is usually stable if the output pole is dominant: p0 ≪ min(non‑dominant poles).
- To increase phase margin with large CL or heavy routing caps:
- Reduce cascode W to trim node capacitances.
- Add a small feed‑forward capacitor Cf from input pair drains (folded node) to output with a series Rz to place a LHP zero: fz ≈ 1/(2πRzCf) near the first non‑dominant pole.
- Exploit CL’s ESR (or add a tiny series resistor 0.5–2 Ω on‑chip in series with CL pad) to generate a stabilizing zero if needed.
- Verify PM in unity‑gain configuration across PVT and CL tolerances.
Step G: Biasing and references
- Generate biases VBP_casc, VBN_casc, VBN_tail with a self‑biased high‑swing cascode mirror. Targets:
- VBN_tail ≈ VGS,N(tail) for Itail at chosen Vov.
- VBN_casc such that the NMOS cascode keeps VDS(sat) ≈ Vov,Ncas across signal swing.
- VBP_casc similarly on PMOS side.
- Provide a clean VCM reference (e.g., VDD/2 or app‑specific) if fully differential with CMFB.
Step H: Output swing check
- With Vov ≈ 150 mV per stacked device:
- Vout,max ≈ 1.8 V − (0.15 + 0.15) ≈ 1.5 V.
- Vout,min ≈ 0 V + (0.15 + 0.15) ≈ 0.30 V.
→ About 1.2 Vpp linear swing on 1.8 V supply.
Step I: Noise and offset quick view
- Input‑referred thermal noise dominated by the input pair:
\[ \overline{v{n,in}^2} \approx \frac{4kT\gamma}{g{m1}}\left(1 + \alpha{fold} + \alpha{load}\right), \]
where α terms are contributions of folding and load devices referred to the input (keep their W small, L long).
- 1/f noise: use longer L and adequate W for input pair; consider PMOS input if flicker dominates at low frequency (trade‑off UGB).
- Offset: size input pair area for Pelgrom AVt target; match current mirrors; use common‑centroid for critical pairs.
Step J: Power
- Example currents: Itail ≈ 84 µA, two folded branches ≈ 2×80 µA, bias mirrors ≈ 30–40 µA → total ≈ 274–284 µA. At 1.8 V: 0.49–0.51 mW (within 1 mW target).
4) Device sizing from currents and chosen Vov (PDK‑agnostic)
- For each device: choose (gm/ID) and Vov. Then:
- Id set by budget above.
- gm = (gm/ID)·Id.
- From your model or gm/ID charts, extract required W/L for given gm/ID, Id, L.
- If using long‑channel approximation for an initial guess:
\[ \frac{W}{L} \approx \frac{2 ID}{\mu C{ox} V_{ov}^2}. \]
- Iterate to hit Vov targets with minimal W to keep parasitics small.
5) Fully differential option and CMFB (if needed)
- A fully differential FC needs a CMFB loop to hold the average of Vout± at VCM,REF.
- Simple continuous‑time CMFB: resistive divider sensing (Vout+ + Vout−)/2 − VCM,REF drives a transconductor that adjusts the PMOS current sources (for NMOS input) to set the common‑mode.
- Ensure CMFB loop UGB is 5–10× below the signal‑path UGB and phase margin ≥ 60°. Check CMFB stability separately (break the CMFB loop and run AC).
6) Non‑dominant pole estimates and practical tuning
- Folded node pole: pF ≈ gm_fold/(2π·Cnode) if the node is low‑impedance; often tens to hundreds of MHz.
- Cascode gate nodes: keep bias networks low‑impedance (use decoupling caps or local mirrors) to avoid slow bias poles coupling in.
Current information and trends
- gm/ID‑based sizing is the industry standard for first‑time‑right analog design; build your own gm/ID and ro/ID charts from your PDK models.
- To push DC gain without sacrificing swing, gain‑boosted cascodes are common; ensure the boost amps have sufficient bandwidth and low noise injection.
- For low‑VDD nodes (<1.2 V), bulk‑driven or inverter‑based input stages are alternatives; for precision, chopper or auto‑zero can be added ahead of the FC core.
- Layout‑aware design (parasitic‑aware iteration with post‑layout extraction) is essential at 65 nm and below.
Supporting explanations and details
- Why NMOS input? Higher mobility → higher gm for given current → higher UGB and lower thermal noise. PMOS input trades lower flicker noise against reduced speed.
- Why long L on cascodes? ro ∝ L (roughly); boosting ro is the cheapest path to higher A0 without extra stages.
- Headroom: FC “folds” the input currents so that the input pair and cascodes are not stacked in series with the output load, enabling large ICMR at low supply compared to telescopic.
Ethical and legal aspects
- Respect your PDK license/NDAs; do not share proprietary model parameters.
- If destined for a product, ensure ESD, latch‑up, and reliability rules (EM/IR, BTI/HCI) are met per your foundry’s sign‑off.
Practical guidelines
- Implementation
- Start with schematic‑level gm/ID design. Build bias generator first; simulate bias independence vs PVT.
- Add ESD clamps and I/O pads early to capture pad capacitance at the output.
- Best practices
- Symmetric layout for input pair and critical mirrors; common‑centroid and dummy fingers.
- Guard rings, local decoupling on bias nodes, shielded routes for sensitive high‑impedance nodes.
- Keep cascode W minimal to reduce C while meeting Vov at your current.
- Challenges and mitigations
- Marginal phase margin: reduce node caps, increase cascode gm (more current or larger W), or add Cf–Rz lead compensation.
- Gain shortfall: lengthen cascodes, reduce currents slightly (raises ro), or add gain‑boosting cascodes.
- Excess 1/f noise: lengthen/upsized input pair or switch to PMOS input.
Possible disclaimers or additional notes
- All numeric examples are first‑pass estimates; exact values depend on your PDK (µCox, λ, Vth, γ, etc.) and will change after parasitics.
- A single‑stage FC generally reaches 70–90 dB gain; if you require >100 dB with large CL at low power, plan for gain‑boosting or a second stage with compensation.
Suggestions for further research
- Build gm/ID and ro/ID charts from your BSIM models (sweep W/L, Id; extract gm/Id, ro, fT).
- Study gain‑boosted cascodes and regulated cascode mirrors; analyze their noise/stability impact.
- Explore chopper or auto‑zero front‑ends if sub‑µV offsets or 1/f noise are critical.
Resources for study (titles only)
- Sansen, Analog Design Essentials (gm/ID method, FC design).
- Razavi, Design of Analog CMOS Integrated Circuits (FC op‑amp chapter).
- Gray, Hurst, Lewis, Meyer, Analysis and Design of Analog ICs (op‑amp theory, CMFB).
Brief summary
- Provide your exact specifications and PDK to finalize device sizes and bias voltages.
- Use UGB → gm1 and SR → Itail/Ifold as the primary drivers; set small Vov for stacked devices and long L on cascodes to meet gain and swing.
- Verify headroom, gain, stability, noise, and mismatch over PVT; iterate with post‑layout extraction.
- If you share your target numbers (VDD, A0, UGB, PM, SR, CL, swing, ICMR, power, node), I will return concrete W/L values, bias voltages/currents, and a simulation checklist tailored to your process.
