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I'm struggling with a signal analysis electrical engineering college assignment. We need to a derive differential equation for a low-pass filter, high-pass filter and a band pass filter (made by connecting the output of a low pass filter to the input of a high pass filter). Here are diagrams for reference:

Low pass filter: enter image description hereLow Pass Filter Image

High pass filter: enter image description hereHigh Pass Filter Image

BandBand Pass Filter$$$$ Band pass filter (buffer can be removed): [img=]

The equations I derived are: - low pass filter: Vo=Vi-RC(dVi/dt) - high pass filter: Vo=RC(dVi/dt) - band pass filter: Vo=R2C2((1-C1-R1)-R1C1(d^2Vi/dt^2))

  • low pass filter: $$V_o=V_i-RC \frac{dV_i}{dt}$$
  • high pass filter: $$V_o=RC \frac{dV_i}{dt}$$
  • band pass filter: $$V_o = R_2C_2 ( (1-C_1-R_1)- R_1C_1 \frac{d^2V_i}{dt^2} )$$

The equation for the band pass filter I found by making the input of the high pass filter the output of the low pass filter. So I derived the equation of the low pass filter with respect to time and got dVo/dt = dVi/dt - R1*dVi/dt - C1*dVi/dt: $$ \frac{dV_o}{dt} = \frac{dV_i}{dt} - R_1\frac{dVi}{dt} - C_1\frac{dV_i}{dt} - R_1C_1\frac{d^2V_i}{dt^2} $$ - R1C1*(d^Vi/dt^2). 

I substituted in this rate of change of voltage into the equation of the high pass filter to get the equation I derived for the band pass filter.

Could anyone please tell me if what I have done is valid and if not, please explain to me what the correct strategy is. Thank you kindly.

I'm struggling with a signal analysis electrical engineering college assignment. We need to a derive differential equation for a low-pass filter, high-pass filter and a band pass filter (made by connecting the output of a low pass filter to the input of a high pass filter). Here are diagrams for reference:

Low pass filter: enter image description here

High pass filter: enter image description here

Band pass filter (buffer can be removed): [img=]

The equations I derived are: - low pass filter: Vo=Vi-RC(dVi/dt) - high pass filter: Vo=RC(dVi/dt) - band pass filter: Vo=R2C2((1-C1-R1)-R1C1(d^2Vi/dt^2))

The equation for the band pass filter I found by making the input of the high pass filter the output of the low pass filter. So I derived the equation of the low pass filter with respect to time and got dVo/dt = dVi/dt - R1*dVi/dt - C1*dVi/dt - R1C1*(d^Vi/dt^2). I substituted in this rate of change of voltage into the equation of the high pass filter to get the equation I derived for the band pass filter.

Could anyone please tell me if what I have done is valid and if not, please explain to me what the correct strategy is. Thank you kindly.

I'm struggling with a signal analysis electrical engineering college assignment. We need to a derive differential equation for a low-pass filter, high-pass filter and a band pass filter (made by connecting the output of a low pass filter to the input of a high pass filter). Here are diagrams for reference:

Low pass filter Low Pass Filter Image

High pass filter High Pass Filter Image

Band Pass Filter$$$$ Band pass filter (buffer can be removed)

The equations I derived are:

  • low pass filter: $$V_o=V_i-RC \frac{dV_i}{dt}$$
  • high pass filter: $$V_o=RC \frac{dV_i}{dt}$$
  • band pass filter: $$V_o = R_2C_2 ( (1-C_1-R_1)- R_1C_1 \frac{d^2V_i}{dt^2} )$$

The equation for the band pass filter I found by making the input of the high pass filter the output of the low pass filter. So I derived the equation of the low pass filter with respect to time and got: $$ \frac{dV_o}{dt} = \frac{dV_i}{dt} - R_1\frac{dVi}{dt} - C_1\frac{dV_i}{dt} - R_1C_1\frac{d^2V_i}{dt^2} $$  

I substituted in this rate of change of voltage into the equation of the high pass filter to get the equation I derived for the band pass filter.

Could anyone please tell me if what I have done is valid and if not, please explain to me what the correct strategy is. Thank you kindly.

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Differential Equation of a Band Pass Filter

I'm struggling with a signal analysis electrical engineering college assignment. We need to a derive differential equation for a low-pass filter, high-pass filter and a band pass filter (made by connecting the output of a low pass filter to the input of a high pass filter). Here are diagrams for reference:

Low pass filter: enter image description here

High pass filter: enter image description here

Band pass filter (buffer can be removed): [img=]

The equations I derived are: - low pass filter: Vo=Vi-RC(dVi/dt) - high pass filter: Vo=RC(dVi/dt) - band pass filter: Vo=R2C2((1-C1-R1)-R1C1(d^2Vi/dt^2))

The equation for the band pass filter I found by making the input of the high pass filter the output of the low pass filter. So I derived the equation of the low pass filter with respect to time and got dVo/dt = dVi/dt - R1*dVi/dt - C1*dVi/dt - R1C1*(d^Vi/dt^2). I substituted in this rate of change of voltage into the equation of the high pass filter to get the equation I derived for the band pass filter.

Could anyone please tell me if what I have done is valid and if not, please explain to me what the correct strategy is. Thank you kindly.