hw_sim v1.1: ENOB-after-cal 8.51b (clears 7.0 bar; per-bit mismatch model) + noise budget 138.7uV vs 100uV floor = MARGINAL -> hardware wall-1 quantified, wants big nudges

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_014FAPDWQ49M5Ye3NpTndTpn

2 files changed, 115 insertions, 0 deletions

diff --git a/hw_sim/NOTES.md b/hw_sim/NOTES.md
index bb616f5..ed5bd75 100644
--- a/hw_sim/NOTES.md
+++ b/hw_sim/NOTES.md
@@ -32,3 +32,17 @@ Candidate fixes to put to the experts, in our preference order:
   (c) accept 3.14 us (5% schedule slip).
 None of this blocks the sim line: v1.1 (mismatch MC / ENOB, noise integration) and stage C
 (SPICE-in-the-loop toy training) proceed independently of which fix wins.
+
+## v1.1 (cell_v11.py, 2026-07-17): ENOB Monte Carlo + noise budget
+A. Per-BIT ladder mismatch MC (sigma_bit 0.4% ~ datasheet +-1 LSB class), per-cell single-scale
+   cal: **ENOB 8.51 b mean, p5 8.34 b — clears the 7.0 screen bar with margin.** The Y3 gray-
+   market screen is realistic. (First model iteration with Thevenin-only structure was vacuous —
+   single-scale cal cancelled it exactly; per-bit structure is the honest model.)
+B. Noise budget at (R_f=1k, C_f=294pF): op-amp 8.7 nV/rtHz x noise-gain peak x16 over the
+   closed-loop band -> **138.7 uV RMS output-referred vs the 0.1 mV contrast floor = 0.7x
+   headroom, MARGINAL.** This is hardware wall-1 with a SPICE number: the contrast signal
+   scales with beta while this floor is fixed -> the machine WANTS big nudges — exactly what
+   the GPU campaign independently concluded (ride-high beta recipes). Mitigations if more
+   headroom needed: post-settle integration window (1/sqrt(T)), read averaging, band-limit
+   after settle, larger VREF. Model caveats: flat op-amp noise only (no 1/f, no Johnson/DAC
+   switch terms — order-checked small at this impedance level).
diff --git a/hw_sim/cell_v11.py b/hw_sim/cell_v11.py
new file mode 100644
index 0000000..897053c
--- /dev/null
+++ b/hw_sim/cell_v11.py
@@ -0,0 +1,101 @@
+"""v1.1: (A) ENOB-after-per-cell-cal Monte Carlo (resistor lot spread + code-dependent R_eq),
+(B) op-amp noise integrated over the closed-loop bandwidth at the v1 operating point
+    (R_f=1k, C_f=294pF) vs the 0.1-1 mV contrast floor.
+DC transfer is algebraic (settled state); SPICE noise via ngspice .noise on the TIA.
+"""
+import os
+os.environ.setdefault('NGSPICE_LIBRARY_PATH', '/home/yurenh2/miniconda3/lib/libngspice.so')
+import numpy as np
+import matplotlib
+matplotlib.use('Agg')
+import matplotlib.pyplot as plt
+from PySpice.Spice.Netlist import Circuit, SubCircuit
+
+rng = np.random.default_rng(7)
+N = 64
+R0 = 11e3
+RF, CF = 1e3, 294e-12
+EN_V = 8.7e-9          # MCP6022 input voltage noise, V/rtHz (flatband)
+FS_CODE = 255
+
+def req_of_code(code, rbase):
+    # datasheet: equivalent output R varies 0.8R..2R with code (excluding all-0s).
+    # smooth monotone proxy between the endpoints:
+    frac = max(code, 1) / 255.0
+    return rbase * (2.0 - 1.2 * frac)
+
+def settled_out(codes, rbases, vref=0.1, rf=RF):
+    # inverting summing node: Vout = -rf * sum(vref*code_i/256 / Req_i(code_i))
+    return -rf * sum(vref * (c / 256.0) / req_of_code(c, rb) for c, rb in zip(codes, rbases))
+
+# ---------- A: per-BIT ladder mismatch -> INL not removable by single-scale cal ----------
+# each DAC's 8 bit-legs carry independent relative errors eps_k; per-cell cal removes only the
+# overall gain; the residual code-shape error IS the INL. sigma_bit set so typical INL ~ datasheet
+# relative accuracy (+-1 LSB class).
+NMC = 400
+SIG_BIT = 0.004
+enob = []
+for _ in range(NMC):
+    eps = rng.normal(0, SIG_BIT, (N, 8))
+    w = (2 ** np.arange(8))[None, :] * (1 + eps)          # per-cell bit weights
+    codes = np.arange(1, 256)
+    bits = ((codes[:, None] >> np.arange(8)[None, :]) & 1)  # 255 x 8
+    val = bits @ w.T                                      # 255 x N raw values
+    ideal = codes.astype(float)[:, None]
+    cal = ideal[-1] / val[-1]                             # per-cell single-scale cal at code 255
+    resid = val * cal[None, :] - ideal                    # LSB units
+    rms = np.sqrt(np.mean(resid ** 2))
+    enob.append(8 - np.log2(max(2 * np.sqrt(3) * rms / 1.0, 1e-9)) - 0)
+enob = np.array(enob)
+inl_p95 = None
+print(f'A: per-bit mismatch sigma {SIG_BIT*100:.1f}% -> ENOB after per-cell cal: '
+      f'mean {enob.mean():.2f} b, p5 {np.percentile(enob,5):.2f} b  [screen bar >=7.0]')
+
+# ---------- B: ngspice noise analysis at the operating point ----------
+class OpAmp(SubCircuit):
+    NODES = ('inp', 'inn', 'out')
+    def __init__(self, name):
+        super().__init__(name, *self.NODES)
+        self.B('gain', 'x', self.gnd, v=f'1e5*(v(inp)-v(inn))')
+        rp = 1e6
+        cp = 1.0 / (2 * np.pi * 100.0 * rp)
+        self.R('p', 'x', 'p1', rp)
+        self.C('p', 'p1', self.gnd, cp)
+        self.B('buf', 'o', self.gnd, v='v(p1)')
+        self.R('out', 'o', 'out', 25)
+
+c = Circuit('noise_col')
+c.subcircuit(OpAmp('opamp'))
+c.SinusoidalVoltageSource('vn', 'np', c.gnd, amplitude=1.0)   # noise injection point (input-referred)
+for i in range(N):
+    c.R(f'w{i}', c.gnd, 'sum', req_of_code(128, R0))
+c.C('bus', 'sum', c.gnd, 64 * 85e-12)
+c.R('f', 'out', 'sum', RF)
+c.C('f', 'out', 'sum', CF)
+c.X('amp', 'opamp', 'np', 'sum', 'out')   # inject at the + input = input-referred source
+sim = c.simulator(temperature=27, nominal_temperature=27)
+an = sim.ac(start_frequency=10, stop_frequency=100e6, number_of_points=30, variation='dec')
+f = np.array(an.frequency)
+gain = np.abs(np.array(an['out']))        # noise gain vs frequency
+# integrate (EN_V * gain)^2 df
+integrand = (EN_V * gain) ** 2
+vn_rms = np.sqrt(np.trapz(integrand, f))
+nbw_gain = np.sqrt(np.trapz(gain ** 2, f) / max(f[-1] - f[0], 1))
+print(f'B: output-referred op-amp noise RMS {vn_rms*1e6:.2f} uV over closed-loop band '
+      f'(peak noise gain {gain.max():.1f}) | contrast floor 0.1 mV -> '
+      f'{"OK" if vn_rms < 1e-4 else "MARGINAL"} (ratio {1e-4/vn_rms:.1f}x headroom)')
+
+# ---------- figure ----------
+fig, axes = plt.subplots(1, 2, figsize=(11.5, 4.2))
+axes[0].hist(enob, bins=30, color='#2c6fbb', alpha=0.85)
+axes[0].axvline(7.0, color='#b03a2e', ls='--')
+axes[0].text(7.0, axes[0].get_ylim()[1]*0.9, ' screen bar 7.0', color='#b03a2e', fontsize=9)
+axes[0].set_xlabel('ENOB proxy after per-cell cal (bits)'); axes[0].set_ylabel('MC count')
+axes[0].set_title(f'A: 400-trial MC, per-bit mismatch 0.4% — mean {enob.mean():.2f} b')
+axes[1].loglog(f, EN_V * gain * 1e9, color='#7b5aa6')
+axes[1].set_xlabel('Hz'); axes[1].set_ylabel('output noise density (nV/√Hz)')
+axes[1].set_title(f'B: op-amp noise → output; integrated RMS {vn_rms*1e6:.1f} µV (floor 100 µV)')
+fig.suptitle('EP column v1.1 — ENOB-after-cal Monte Carlo + noise budget (datasheet-anchored)', fontsize=11)
+fig.tight_layout()
+fig.savefig('/home/yurenh2/ept/assets/figs/fig_spice_v11.png', dpi=150)
+print('DONE_SPICE_V11')