This article shows a transistor audio filter.

The filter is made from three Darlington pair transistor voltage followers.

Step 1: Design the Circuit

Connecting two of more capacitors in parallel reduces the current dissipation across each capacitor.

Calculate transistor input resistance Beta*re:

Beta*reB = Beta * (26*10^-3) / Ie

= Beta * (26*10^-3) / (Vs / 2 / Re1)

= 100 * (26*10^-3) / (1.5 V / 2 / 10,000 ohms)

= 17,333.3333333 ohms

Beta*reA = Beta * (26*10^-3) / (Ie / Beta)

= Beta * (26*10^-3) / (Vs / 2 / Re1 / (Beta + 1))

= 100 * (26*10^-3) / (1.5 V / 2 / 10,000 ohms / 101)

= 1,750,666.66667 ohms

= 1.75 Megohms

Calculate input resistance of the Darlington pair transistor voltage follower:

(We are ignoring the transistor input resistance Beta*re)

Ri = (Beta + 1)*(Beta + 1) * Re = 101 * 101 * 10,000 ohms

= 102,010,000 ohms = 102.01 Megohms

The transistor input resistance Beta*re will only add to the total voltage follower input resistance.

Calculate output resistance of the Darlington pair transistor voltage follower:

(We are ignoring the transistor resistance Beta*re)

Ro = Re || ((Rb1a || Rb2b) / (Beta + 1) / (Beta + 1))

= 10,000 ohms || (((1*10^6 ohms)||(10*10^6 ohms)) / 101 / 101)

= 88.3306392488 ohms

The transistor input resistance Beta*re will increase the output resistance slightly.

Calculate minimum low pass filter frequency:

FlpfMin = 1 / (2*pi*(Rlp1 + Rlp2)*(Clp1 + Clp2))

= 1 / (2*pi*(1,010,000 ohms)*(2*10^-9))

= 78.7895757881 Hz

Calculate maximum low pass filter frequency:

FlpfMax = 1 / (2*pi*Rlp1*(Clp1 + Clp2))

= 1 / (2*pi*(10,000 ohms)*(2*10^-9))

= 7,957.74715459 Hz

Calculate minimum high pass filter frequency:

FhpfMin = 1 / (2*pi*(Rhp1 + Rhp2)*Chp)

= 1 / (2*pi*1,001,000 ohms*(47*10^-9))

= 3.38289249244 Hz

Calculate maximum high pass filter frequency:

FhpfMax = 1 / (2*pi*Rhp1*Chp)

= 1 / (2*pi*1,000 ohms*(47*10^-9))

= 3,386.27538493 Hz

Step 2: Simulations

Transient 1:

Transient 2:

Full Spectrum Bandwidth:

Spectrum Low Pass Filter (LPF):

Spectrum High Pass Filter (HPF):