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| author | Philipp Le <philipp-le-prviat@freenet.de> | 2020-06-09 00:14:41 +0200 |
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| committer | Philipp Le <philipp-le-prviat@freenet.de> | 2021-03-04 22:44:39 +0100 |
| commit | 87fb339206b7be9db51104ce4559c3c0879541e2 (patch) | |
| tree | 68245259a88f4a51e3bbd6ca1f64821ed02fd2b1 /chapter05/content_ch05.tex | |
| parent | afed1ed6b62aa9e0c347e608d57d3ae9118e80ca (diff) | |
| download | dcs-lecture-notes-87fb339206b7be9db51104ce4559c3c0879541e2.zip dcs-lecture-notes-87fb339206b7be9db51104ce4559c3c0879541e2.tar.gz dcs-lecture-notes-87fb339206b7be9db51104ce4559c3c0879541e2.tar.bz2 | |
Added solutions of Exercise 5
Diffstat (limited to 'chapter05/content_ch05.tex')
| -rw-r--r-- | chapter05/content_ch05.tex | 2 |
1 files changed, 1 insertions, 1 deletions
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} |