$$\dfrac{U(s)}{C(s)}$$

$$\dfrac{C(s)}{U(s)}$$

$$U(s) \cdot C(s)$$

$$\dfrac{C^2(s)}{U(s)}$$

어떤 계의 전달 함수는 그 계에 대한 임펄스 응답의 라플라스 변환과 같다.

전달 함수 $P(s)$인 계의 입력이 임펄스 함수( $\delta$함수)이고 모든 초기값이 0이면 그 계의 출력 변환은 $P(s)$와 같다.

계의 전달 함수는 계의 미분 방정식을 라플라스 변환하고 초기값에 의하여 생긴 항을 무시하면 $P(s)= \mathcal{L}^{-1} \left[ \dfrac{Y^2}{X^2} \right]$와 같이 얻어진다.

계 전달 함수의 분모를 0으로 놓으면 이것이 곧 특성 방정식이 된다.

$$\dfrac{1}{Ts^2+1}$$

$$\dfrac{1}{Ts+1}$$

$${Ts^2+1}$$

$${Ts+1}$$

$$C_1 + C_2$$

$$\dfrac{C_2}{C_1}$$

$$\dfrac{C_1}{C_1+C_2}$$

$$\dfrac{C_2}{C_1+C_2}$$

0

0.5

1

0.707

$$\dfrac{LC}{1+LCs}$$

$$\dfrac{LC}{1+LCs^2}$$

$$\dfrac{1}{1+LCs}$$

$$\dfrac{1}{1+LCs^2}$$

$$\dfrac{s}{R+Ls}$$

$$\dfrac{1}{s+ \dfrac{R}{L}}$$

$$\dfrac{1}{R+Ls}$$

$$\dfrac{s}{s+ \dfrac{R}{L}}$$

$$\dfrac{Rs}{s+CR}$$

$$\dfrac{Cs}{Cs+R}$$

$$\dfrac{Cs}{CRs+1}$$

$$\dfrac{s}{s+\dfrac{1}{CR}}$$

$$\dfrac{R}{RCs+1}$$

$$\dfrac{C}{RCs+1}$$

$$\dfrac{RC}{RCs+1}$$

$$\dfrac{RCs}{RCs+1}$$

$$\dfrac{LCs^2+1}{LCs^2-1}$$

$$\dfrac{1}{LCs^2+1}$$

$$\dfrac{1}{LCs^2-1}$$

$$\dfrac{LCs^2-1}{LCs^2+1}$$

$$\dfrac{1}{1+RCs}$$

$$\dfrac{RCs}{1+RCs}$$

$$\dfrac{1+RCs}{1-RCs}$$

$$\dfrac{1-RCs}{1+RCs}$$

$$\dfrac{LRs}{LCs^2+RCs+1}$$

$$\dfrac{Cs}{LCs^2+RCs+1}$$

$$\dfrac{RCs}{LCs^2+RCs+1}$$

$$\dfrac{LRCs}{LCs^2+RCs+1}$$

$$\dfrac{s}{LCs^2+RCs+1}$$

$$\dfrac{1}{LCs^2+RCs+1}$$

$$\dfrac{Ls}{LCs^2+RCs+1}$$

$$\dfrac{Cs}{LCs^2+RCs+1}$$

$$\dfrac{(R_1+R_2)C_2s+1}{R_2C_2s+1}$$

$$\dfrac{R_2C_2s+1}{(R_1+R_2)C_2s+1}$$

$$\dfrac{R_2C_2+1}{(R_1+R_2)C_2s+1}$$

$$\dfrac{(R_1+R_2)C_2+1}{R_2C_2s+1}$$

$$\dfrac{j \omega}{(5-\omega^2)+j \omega}$$

$$\dfrac{j \omega}{(5+\omega^2)+j \omega}$$

$$\dfrac{j \omega}{(5-\omega)^2+j \omega}$$

$$\dfrac{j \omega}{(5+\omega)^2+j \omega}$$

$$\dfrac{R}{R_1Cs+1}$$

$$\dfrac{s+1}{s+(R_1+R_2)+R_1R_2C}$$

$$\dfrac{R_1R_2s+RCs}{R_1Cs+R_1R_2s^2+C}$$

$$\dfrac{R_2+R_1R_2Cs}{R_2+R_1R_2Cs+R_1}$$

$$\dfrac{T_1}{T_2s+1}$$

$$\dfrac{T_2s}{T_1s+1}$$

$$\dfrac{T_1s+1}{T_2s+1}$$

$$\dfrac{T_1(T_1s+1)}{T_2(T_2s+1)}$$

$$\dfrac{1}{CRs+1+\dfrac{R}{R_L}}$$

$$\dfrac{1}{CRs+\dfrac{R}{R_L}}$$

$$\dfrac{1}{\dfrac{s}{CR}+1+\dfrac{R}{R_L}}$$

$$\dfrac{1}{\dfrac{s}{CR}+\dfrac{R}{R_L}}$$

$$\dfrac{1}{s+ \dfrac{C_1+C_2}{R_1C_1s}}$$

$$\dfrac{RC_1C_2s}{R_1C_1s+ \dfrac{C_1+C_2}{R_1C_1C_2}}$$

$$\dfrac{R_1(C_1+C_2)s}{R_1C_2s+ R_1C_1C_2s^2} \left( \dfrac{1}{R_1C_1C_2} \right)$$

$$\dfrac{1}{s+ \dfrac{C_1+C_2}{R_1C_1C_2}} \left( \dfrac{1}{R_1C_1} \right)$$

$$\dfrac{1}{5} \cdot \dfrac{s^2+5}{s^2 + s + 5}$$

$$\dfrac{1}{10} \cdot \dfrac{2s+5}{s^2 + 2s + 5}$$

$$\dfrac{1}{10} \cdot \dfrac{2s^2+15}{s^2 + 2s + 3}$$

$$\dfrac{1}{5} \cdot \dfrac{s^2+5}{s^2 + s + 1}$$

$$\dfrac{s+30}{s+25}$$

$$\dfrac{30}{s+25}$$

$$\dfrac{s}{s+25}$$

$$\dfrac{s}{3s+50}$$

1

0.1

0.01

0.001

$$\dfrac{K}{s}$$

$${K}{s}$$

$${1+Ks}$$

$$\dfrac{K}{1+s}$$

미분 회로

적분 회로

가산 회로

미분, 적분 회로

$$\dfrac{s}{a_2s^2+a_1s+a_3}$$

$$\dfrac{1}{a_2s^2+a_1s+a_3}$$

$$\dfrac{s}{a_3s^2+a_2s+a_1}$$

$$\dfrac{1}{a_3s^2+a_2s+a_1}$$

$$\dfrac{s+2}{3s^2+s+1}$$

$$\dfrac{s+1}{2s^2+s+3}$$

$$\dfrac{s+1}{s^2+3s+2}$$

$$\dfrac{s+1}{s^2+s+3}$$

$$G(s)=\dfrac{s^2+3s+2}{s+1}$$

$$G(s)=\dfrac{2s+1}{s^2+s+1}$$

$$G(s)=\dfrac{s+1}{s^2+3s+2}$$

$$G(s)=\dfrac{s^2+s+1}{2s+1}$$

$$\dfrac{s-5}{6s^2+3s-2}$$

$$\dfrac{s+5}{6s^2-3s+2}$$

$$\dfrac{s-5}{6s^3+3s^2-2s}$$

$$\dfrac{s+5}{6s^3+3s^2+2s}$$

$$\dfrac{1}{(s+2)(s+3)}$$

$$\dfrac{s+1}{(s+2)(s+3)}$$

$$\dfrac{s+4}{(s+2)(s+3)}$$

$$\dfrac{s}{(s+2)(s+3)}$$

$$\dfrac{d}{dt}r(t)+4r(t)=x(t)$$

$$\int r(t)dt+4r(t)=x(t)$$

$$\dfrac{d}{dt}x(t)+4x(t)=r(t)$$

$$\int x(t)dt+4x(t)=r(t)$$

$$P(s) = \dfrac{Y(s)}{X(s)} = \dfrac{e^{-sT}}{s+1}$$

$$P(s) = \dfrac{X(s)}{Y(s)} = \dfrac{e^{sT}}{s-1}$$

$$P(s) = \dfrac{X(s)}{Y(s)} = \dfrac{s+1}{e^{sT}}$$

$$P(s) = \dfrac{Y(s)}{X(s)} = \dfrac{e^{-2sT}}{s+1}$$

$$\dfrac{da(t)}{dt}+2a(t)=2b(t)$$

$$2\dfrac{da(t)}{dt}+a(t)=2b(t)$$

$$\dfrac{da(t)}{dt}+2a(t)=b(t)$$

$$2\dfrac{da(t)}{dt}+a(t)=b(t)$$

$$y(t)=\dfrac{1}{2} \dfrac{d^2x(t)}{dt^2}+\dfrac{dx(t)}{dt}+\dfrac{1}{2}x(t)$$

$$y(t)=2 \dfrac{dx(t)}{dt}+x(t)+\int x(t)dt$$

$$y(t)=\dfrac{dx(t)}{dt}+x(t)+1$$

$$2x(t)=\dfrac{d^2y(t)}{dt^2}+2\dfrac{dy(t)}{dt}+y(t)$$

$$\dfrac{d^2}{dt^2}e_0(t)+3\dfrac{d}{dt}e_0(t)+e_0(t)=e_i(t)$$

$$\dfrac{d^2}{dt^2}e_i(t)+3\dfrac{d}{dt}e_i(t)+e_i(t)=e_0(t)$$

$$\dfrac{d^2}{dt^2}e_i(t)+3\dfrac{d}{dt}e_i(t)+\int e_i(t)dt=e_0(t)$$

$$\dfrac{d^2}{dt^2}e_0(t)+3\dfrac{d}{dt}e_0(t)+\int e_0(t)dt=e_i(t)$$

$$\dfrac{d^2}{dt^2}x(t) +3\dfrac{d}{dt}x(t) +2x(t) = 10y(t)$$

$$\dfrac{d^2}{dt^2}x(t) +3\dfrac{d}{dt}x(t) +2x(t) = 10$$

$$\dfrac{d^2}{dt^2}y(t) +3\dfrac{d}{dt}y(t) +2y(t) = 10x(t)$$

$$\dfrac{d^2}{dt^2}y(t) +3\dfrac{d}{dt}y(t) +2y(t) = 10$$

$$\dfrac{d^2c(t)}{dt^2} +3\dfrac{dc(t)}{dt}+c(t)=\dfrac{dr(t)}{dt}+r(t)$$

$$\dfrac{d^2c(t)}{dt^2} +\dfrac{dc(t)}{dt}+c(t)=\dfrac{dr(t)}{dt}+r(t)$$

$$3\dfrac{d^2c(t)}{dt^2} +\dfrac{dc(t)}{dt}+c(t)=\dfrac{dr(t)}{dt}+r(t)$$

$$\dfrac{d^2c(t)}{dt^2} +3\dfrac{dc(t)}{dt}+3c(t)=2\dfrac{dr(t)}{dt}+r(t)$$

$$\dfrac{1}{s^2+1}, \quad \dfrac{d^2y}{dt^2}+y=x$$

$$\dfrac{1}{s^2-1}, \quad \dfrac{d^2y}{dt^2}+2y=2x$$

$$\dfrac{1}{2s+1}, \quad \dfrac{d^2y}{dt^2}-y=x$$

$$\dfrac{1}{2s^2-1}, \quad \dfrac{d^2y}{dt^2}-2y=2x$$

$$\dfrac{s}{s+2}$$

$$\dfrac{s}{s^2+2}$$

$$\dfrac{2}{s^2+2}$$

$$\dfrac{2}{s^2+4}$$