# How can I plot the frequency response of the equation below using MATLAB?

$$\boxed{\dfrac{V_{\text{out}}(j\omega)}{V_{\text{in}}(j\omega)}=\dfrac{2\times10^9}{(1+10j\omega)(100\times10^3j\omega+20\times10^3j\omega+2\times10^9-20\times10^3j\omega}}$$

and $$\dfrac{V_{\text{out}}(j\omega)}{V_{\text{in}}(j\omega)}=\dfrac{j\omega LR_1R_2}{(j\omega L)((1+j\omega C R_2)(j\omega LR_2+j\omega LR_1+R_1R_2)-j\omega LR_1)}$$

I am having a hard time figuring out how can I translate them into symbolic math or what I will do to them to get their frequency response plots.

• Do you know how to plot some function of a single variable? Symbolic math is not required here. Commented Oct 5, 2021 at 14:04
• It's been a moment since I used MATLAB but you could define in the terminal or in a script $s=tf('s');$ and then you replace 'jw' in your equation with 's'. If you call your transfer function T, then all you need to do is $bode(T)$ and it should plot the magnitude and phase responses.
– Big6
Commented Oct 5, 2021 at 14:15

You can use vectors to represent a transfer function in MATLAB, and then you can use the bode(sys) function to plot the magnitude and phase response

b = 2e9;
a = conv([10 1],[1e5 2e9]);
sys = tf(b,a);
bode(sys);


If you want to do it from scratch, you can create a vector of frequencies and plot the function against them.

w = logspace(0,8,200);
sys = 2e9/((10*j*w + 1)*(1e5*j*w + 2e9));
mag = abs(sys);
semilogx(w,mag);


If you’re new to MATLAB you may need to go to the Mathworks Website to see what some of these functions do.