How to find 3db lower and upper frequency bound for frequency response of this problem?

Hello guys, I want to find the 3db upper and lower frequency(Hz) bound for the frequency response of below described code. I have plotted the frequency response(Bandwidth) but how to get the 3db point change. Following is the code of the problem:

    clear all
    clc
    frequency=[10 50 100 200 500 1*10^3 2*10^3 5*10^3 10*10^3 20*10^3 50*10^3 100*10^3 200*10^3 500*10^3 1*10^6 2*10^6 7*10^6 8*10^6 9*10^6 11*10^6 12*10^6 15*10^6 17*10^6 18*10^6 20*10^6 22*10^6 25*10^6 27*10^6 30*10^6]; %Frequency in Hz
    vi=[84 88 92 88 88 88 88 88 88 88 88 88 88 88 88 88 43 43 47 43 43 46 47 47 48 48 43 43 45]; %Input voltage
    vo=[109 390 600 770 880 940 960 980 980 960 1010 1010 1010 1010 980 940 370 350 320 290 270 230 210 190 180 170 130 120 110]; %Output voltage
    gain=( vo./vi) %Finds the gain for respective voltage values
    figure(1)
    semilogx(frequency,gain) % Plots the frequency response of the system

Answer 1

[Star Strider]

The -3 dB points are by definition the half-power points (that’s my understanding), so the easiest way is to calculate the power, find their approximate location and then let interp1 calculate them exactly. If your definition of the -3 dB points is different, you can easily adapt my code.

The Code:

pwr = gain.^2;                                                          % Power
hpp = max(pwr/2);                                                       % Half-Power Points
zci = @(v) find(v(:).*circshift(v(:), [-1 0]) <= 0);                    % Returns Approximate Zero-Crossing Indices Of Argument Vector
db3idx = zci(pwr-hpp);

for k1 = 1:size(db3idx,1)
    idxrng = db3idx(k1):db3idx(k1)+1;
    db3(k1) = interp1(pwr(idxrng), frequency(idxrng), hpp, 'spline','extrap');
end

figure(1)
semilogx(frequency,gain) % Plots the frequency response of the system
hold on
plot(db3, [1 1]*sqrt(hpp), '+r', 'MarkerSize',10)
hold off
grid
legend('Gain', 'Half-Power Points', 'Location','S')

The Plot"

[Hitesh Suthar]

Thanks ! Star Strider. It is exactly what I needed.

[Star Strider]

My pleasure!