Gm Over Id

GBW = gm₁ / (2π · CL)
→ gm₁ = 2π · GBW · CL · 1.2  (1.2倍裕量考虑寄生)

Step 2: 选择 gm/Id（增益-带宽折中）

Step 3: 查表得 Id → 计算 W

Id_need = gm / (gm/Id)
id_sim  = lookup(gm/Id, L)   ← 查找表中 W=1µm 时的绝对电流 (A)

W = Id_need / id_sim * W_tb  (W_tb = 1µm)
  = Id_need / id_sim          (结果单位 µm)

例: gm/Id=14, L=500n → id_sim=5.01µA (at W=1µm)
    Id_need=13.5µA → W = 13.5/5.01 × 1 = 2.7µm

注意: lookup JSON 中的 id 是绝对电流（A），不是电流密度。 idw 字段已废弃，直接用 id / w_testbench 计算。

Step 4: 选择 L（增益-速度折中）

• L 大 → 增益高、速度低
• L 小 → 增益低、速度高
• 经验：L_min ~ 2×L_tech 起步

用 virtuoso-cli 自动化仿真

1. 生成 gm/Id 查找表（单管 DC 仿真）

需要一个单管 testbench（NMOS 或 PMOS），扫描 VGS，提取 oppoint 参数。

# 设置仿真
virtuoso sim setup --lib <LIB> --cell <GMID_TB> --view schematic
virtuoso skill exec 'resultsDir("/tmp/gmid_lookup")'
virtuoso skill exec 'desVar("L" 200e-9)'

# DC 扫描 VGS
virtuoso sim run --analysis dc --param saveOppoint=t --timeout 120

# 提取关键参数 (在每个 VGS 偏置点)
virtuoso sim measure --analysis dcOp \
  --expr 'value(getData("/NM0:gm" ?result "dcOpInfo"))' \
  --expr 'value(getData("/NM0:ids" ?result "dcOpInfo"))' \
  --expr 'value(getData("/NM0:gds" ?result "dcOpInfo"))' \
  --expr 'value(getData("/NM0:vth" ?result "dcOpInfo"))' \
  --expr 'value(getData("/NM0:cgs" ?result "dcOpInfo"))'

2. 生成完整曲线（参数扫描 L）

# 用 SKILL 直接生成 waveVsWave 查找曲线
virtuoso skill exec '
  ;; 确保 DC 结果已加载
  selectResult(quote(dc))
  
  ;; gm/Id vs gain (self_gain = gm/gds)
  waveVsWave(?x OS("/NM0" "gmoverid") ?y OS("/NM0" "self_gain"))
'

virtuoso skill exec '
  ;; gm/Id vs Id/W (电流密度，对数坐标更直观)
  waveVsWave(?x OS("/NM0" "gmoverid") ?y (OS("/NM0" "id") / VAR("W")))
'

virtuoso skill exec '
  ;; gm/Id vs Vov
  waveVsWave(?x OS("/NM0" "gmoverid") ?y (OS("/NM0" "vgs") - OS("/NM0" "vth")))
'

virtuoso skill exec '
  ;; gm/Id vs lambda (沟道长度调制系数)
  waveVsWave(?x OS("/NM0" "gmoverid") ?y (OS("/NM0" "gds") / OS("/NM0" "id")))
'

3. 从查找表读取设计参数

# 已知 gm/Id = 10，L = 200n，查 Id/W
virtuoso skill exec '
  selectResult(quote(dc))
  let((gmid_wave idw_wave)
    gmid_wave = OS("/NM0" "gmoverid")
    idw_wave = OS("/NM0" "id") / VAR("W")
    cross(waveVsWave(?x gmid_wave ?y idw_wave) 10 1 "falling")
  )
'

# 已知 gm/Id = 10，L = 200n，查 gain
virtuoso skill exec '
  selectResult(quote(dc))
  let((gmid_wave gain_wave)
    gmid_wave = OS("/NM0" "gmoverid")
    gain_wave = OS("/NM0" "self_gain")
    cross(waveVsWave(?x gmid_wave ?y gain_wave) 10 1 "falling")
  )
'

4. PMOS 仿真（注意 abs）

# PMOS 的 Id 和 gds 为负值，需要取绝对值
virtuoso skill exec '
  waveVsWave(?x OS("/PM0" "gmoverid") ?y OS("/PM0" "self_gain"))
'
virtuoso skill exec '
  waveVsWave(?x OS("/PM0" "gmoverid") ?y abs(OS("/PM0" "id") / VAR("W")))
'

设计实例：二级 OTA

规格

• GBW = 10 MHz, CL = 10 pF, Gain > 60 dB

Step 1: 输入对管 gm

gm₁ = 2π × 10M × 12p = 753.6 µS

Step 2: 选 gm/Id = 12 (中等反型，增益-速度平衡)

Id₁ = gm₁ / (gm/Id) = 753.6µ / 12 = 62.8 µA

Step 3: 查表 Id/W (L=500n 时)

# 假设查得 Id/W = 2.5 µA/µm
W₁ = Id₁ / (Id/W) = 62.8 / 2.5 = 25.1 µm

Step 4: 验证增益

# 查得 gain(gm/Id=12, L=500n) ≈ 35
# 两级总增益 ≈ 35 × 35 = 1225 ≈ 62 dB ✓

设计指导原则

Ocean SKILL 代码参考

;; 完整的 gm/Id 查找表仿真设置 (NMOS)
simulator('spectre)
design("LIB" "gmid_nmos_tb" "schematic")
resultsDir("/tmp/gmid_nmos")
analysis('dc ?saveOppoint t)
save('all)

;; 仿真输出定义
ocnxlOutputSignal("gmoverid" ?plot t
  ?expr "OS(\"/NM0\" \"gmoverid\")")
ocnxlOutputSignal("self_gain" ?plot t  
  ?expr "OS(\"/NM0\" \"self_gain\")")
ocnxlOutputSignal("id_over_w" ?plot t
  ?expr "OS(\"/NM0\" \"id\") / VAR(\"W\")")
ocnxlOutputSignal("fT" ?plot t
  ?expr "OS(\"/NM0\" \"ft\")")

;; 参数扫描 L
paramAnalysis("L" ?values '(200n 300n 500n 1u 2u))

run()

关键陷阱

• gm/Id 查找表与工艺强相关 — 换工艺必须重新仿真
• L 对 gain 影响巨大 — 必须同时扫描 L
• PMOS Id/gds 为负 — 用 abs() 取绝对值
• 短沟道 gm/Id 曲线偏离理想 — 这正是查表法的优势
• W 初始值影响结果 — 仿真时 W 取中间值，最后根据计算结果微调后重仿
• 体效应 — 仿真 testbench 中 B 端接法要与实际电路一致
• self_gain 不可用时 — 手动用 gm/gds 替代：OS("/NM0","gm")/OS("/NM0","gds")