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diff --git a/chapter05/content_ch05.tex b/chapter05/content_ch05.tex index 59be259..adf043f 100644 --- a/chapter05/content_ch05.tex +++ b/chapter05/content_ch05.tex @@ -1295,7 +1295,7 @@ The non-linearity $M(x)$ of the diode or any other non-linear devices can be exp \begin{equation} \begin{split} x_{o} &= M(x_{i} + x_{LO} + a) = \sum\limits_{n=0}^{\infty} \frac{1}{n!} \left.\frac{\mathrm{d}^n M(x)}{\mathrm{d} x^n}\right|_{x=a} \left(x_{i} + x_{LO} + a - a\right)^n \\ - &= M(a) + \underbrace{M^{(1)}(a) \left(x_{i} + x_{LO}\right)}_{\text{Linear term}} + \underbrace{\frac{M^{(2)}(a)}{2} \left(x_{i} + x_{LO}\right)^2}_{\text{Quadratic term}} + \underbrace{\frac{M^{(3)}(a)}{6} \left(x_{i} + x_{LO}\right)^2}_{\text{Qubic term}} + \dots + &= M(a) + \underbrace{M^{(1)}(a) \left(x_{i} + x_{LO}\right)}_{\text{Linear term}} + \underbrace{\frac{M^{(2)}(a)}{2} \left(x_{i} + x_{LO}\right)^2}_{\text{Quadratic term}} + \underbrace{\frac{M^{(3)}(a)}{6} \left(x_{i} + x_{LO}\right)^3}_{\text{Qubic term}} + \dots \end{split} \end{equation} |