\[N = 16\left(\frac{t_R}{w_b}\right)^2 = 5.54\left(\frac{t_R}{w_{1/2}}\right)^2,\qquad H = \frac{L}{N}\]
含义Meaning
衡量色谱柱效：塔板数越多、塔板高度越小，峰越窄。来源于把色谱柱比作精馏塔的“塔板理论”（马丁与辛格，1941）。
Column efficiency: more plates (smaller plate height) give narrower peaks. From the plate theory comparing a column to a distillation tower (Martin and Synge, 1941).
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(w_b\) | 峰底宽（切线法，= 4σ）base width (= 4σ) | min |
| \(w_{1/2}\) | 半高峰宽（= 2.355σ）width at half height (= 2.355σ) | min |
| \(L\) | 柱长column length | cm |
| \(H\) | 塔板高度（HETP）plate height | cm |
推导Derivation
高斯峰：\(N = (t_R/\sigma)^2\)，即峰的相对方差的倒数。
For a Gaussian peak \(N = (t_R/\sigma)^2\).
峰底宽 4σ ⇒ \(N = 16(t_R/w_b)^2\)；半高宽 \(2\sqrt{2\ln2}\,\sigma = 2.355\sigma\) ⇒ 系数 5.54。
Base width 4σ gives 16; half-height width 2.355σ gives 5.54.
峰宽 ∝ \(\sqrt L\) 而保留时间 ∝ L，所以 N ∝ L。
σ grows as √L while t_R ∝ L, so N ∝ L.
适用条件与局限Assumptions & limitations
只适用于对称高斯峰；拖尾峰需用矩法或福利–多尔西公式。
Gaussian peaks only; tailing needs moments or Foley–Dorsey.