Frequency Response (Bode Plot) with MATLAB

Transcription

1 Frequency Response (Bode Plot) with MATLAB 黃馨儀 216/6/15 適應性光子實驗室

2 常用功能選單 File 選單上第一個指令 New 有三個選項 : M-file Figure Model 開啟一個新的檔案 (*.m) 用以編輯 MATLAB 程式 開始一個新的圖檔 開啟一個新的 simulink 檔案 Help MATLAB Help 查詢相關函式

3 MATLAB 主視窗 Current directory Work space Command window Command history

4 Transfer Function The transfer function H(s) is the ratio of the output response Y(s) to the input response X(s), assuming all the initial conditions are zero. Y ( s) H ( s) = X ( s) H(s) is the Laplace transform of the impulse response function h(t). 1 H() s = Lht () ht () = L H() s [ ] [ ] If X(ω), H(ω) and Y(ω) are the Fourier transforms of x(t), h(t), and y(t), respectively, then [ ] Y( ω) = F ht ( ) xt ( ) = H( ω) X( ω)

5 Frequency Response Frequency Response H(ω) of a Circuit: The transfer function of a circuit is the frequency-dependent ratio of the Fourier transform of an output Y(ω) (an element voltage or current ) to the Fourier transform of an input X(ω) (source voltage or current). Y ( ω) H ( ω) = j H( ω) H( ω) = H( ω) e X ( ω) It is the variation in a circuit s behavior with change in signal frequency and may also be considered as the variation of the magnitude and phase with frequency. A zero, as a root of the numerator polynomial, is a value that results in a zero value of the function. A pole, as a root of the denominator polynomial, is a value for which the function is infinite. N( ω) H ( ω) = D( ω)

6 Frequency Response of Lowpass Filter Example: For the RC circuit shown below, obtain the frequency response V ( ω)/ V ( ω). o s Vo ( ω) 1 jωc 1 H ( ω) = = = V ( ω) R + 1 jωc 1+ jωrc i 1 ω H ω = H ω = ω = RC 1 ( ), ( ) tan, ( ωω) ω Low-pass filter (LPF) 6

7 Bode Plot

8 Example

9 Bode Plot for Example Magnitude H() s = s 2 2s + 12s+ 2 Phase

10 Bode Plot with Matlab H() s = s 2 2s + 12s+ 2 num = [2 ] den = [1 12 2] figure; bode(num,den) grid on Magnitude (db) Phase (deg) Bode Diagram Frequency (rad/sec)

11 Bode Plot with Matlab H() s = s 2 2s + 12s+ 2 num = [2 ] den = [1 12 2] w = logspace(-2,2,1); figure;bode(num,den,w) grid on Magnitude (db) y = logspace(a,b,n) generates n points between decades 1^a and 1^b. Phase (deg) Bode Diagram Frequency (rad/sec)

12 Example R = 2 kω, L = 2 H, C = 2 μf H() s = R s RLC sl R

13 Bode Plot H() s R = 2; L = 2; C = 2e-6; num = [R]; den = [R*L*C L R]; H = tf(num,den) figure; bode(num,den) grid on Magnitude (db) Phase (deg) = Transfer function: s^2 + 2 s s RLC sl R R + + Bode Diagram Frequency (rad/sec)

14 繪圖指令 (1/3) 1. plot ( x, y ) : 以 x 向量之值當橫座標,y 向量之值當縱座標 2. subplot ( m, n, p ) : 將 figure 分割成 m n 的矩陣,p 為 position 3. title ( string ) : 設定圖的名稱 4. xlable ( string ) : 設定圖的 x 軸名稱 5. ylable ( string ) : 設定圖的 y 軸名稱 6. figure ( index ) : 開新圖面 7. Grid : 產生格線 8. hold on ; hold off ; 9. text ( x, y, NCKU) : 在座標 ( x, y ) 上印出 NCKU 1. Gtext ( NCKU ) : 用滑鼠直接選定位置來印出 NCKU 11. loglog ( x, y ) : x 軸與 y 軸座標均以對數比列來繪製 12. semilogx ( x, y ) : x 軸座標均以對數比列來繪製 13. y 軸座標以線性比列來繪製 14. polar ( θ, ρ ) : 畫極座標圖

15 繪圖指令 (2/3)

16 繪圖指令 (3/3) Example : 利用橢圓的參數式來繪出兩個不同樣式的橢圓 t = : pi / 1 : 2 * pi ; % 設 t 為由 ~2pi 每點間隔為 pi/1 之數列 x = sin ( t ) ; y1 =.8 * cos ( t ) ; y2 = 1.5 * cos ( t ) ; plot ( x, y1, m-, x, y2, c* ), grid % 繪圖 Ellipse Graph title ( Ellipse Graph ) % 標題 1.5 xlabel ( x=sin(t) ) ; % 橫軸標註 1 ylabel ( 'y=b*cos(t) ) ; % 縱軸標註.5 y=b*cos(t) x=sin(t)

17 Practice R = 3 kω L = 5 H C = 1 μf H() s = & Bode Plot? 2 s RLC? 2 s RLC + sl + R