I am from electronics background. I have a simple mathematical problem which seems daunting for me.
The general equations for calculating charge is given below. It integrates the capacitance C(v) over the range of voltage 'v'
q(v) = ∫ C(v)dv. limits are from 0 to v (Charge eqn)
Now to obtain the current from this charge the following equation holds true
and i(t) = dq(v(t))/dt . (current eqn).
Now I have a charge which is constant over different range of the voltage. So I dont know how to integrate over the voltage to find the total charge which when differentiated will give me the current.
The following is the value of the capacitance C_GS, C_GD that are dependent on voltages v_GS and v_GD.
C_sov, C_dov and C_ch are constants.
if (v_GS > vth) //cut-off region
C_GS = C_sov + 0;
C_GD = C_dov + 0;
else if ((v_DS) > v_GS-vth) // saturation region
C_GS = C_ch/2+C_sov;
C_GD = C_ch/2+C_dov;
else // linear region
C_GS = (2/3)*C_ch+C_sov;
C_GD = C_ch/3+C_dov;
Now I need to find the charge
q_g = ∫ C_GS(v_GS)dv in the range o to v_GS
q_d = ∫ C_DS(v_DS)dv in the range o to v_DS
With these values, I can differntiate to get the respective currents. The problem is with calculating the charges q_d and q_g.
Could somone help me in deriving the equations for q_d, q_g for the above case? Thanking you in advance.