1.8 Other Second Order Circuits

Second order circuits are not restricted to series RLC and parallel GLC circuits. Other second order circuits include amplifiers and filters. It is beyond the scope of this text to analyze such circuits in detail. In this section we will use the following example to illustrate the transient analysis of a second order active low-pass filter.

Example 1.7

The circuit of Figure 1.19 a known as a Multiple Feed Back (MFB) active low-pass filter. For this circuit, the initial conditions are v _C1 = v _C2 = 0. Compute and sketch v _out( t) for t > 0.

Figure 1.19: Circuit for Example 1.7

Solution:

At node v ₁:

At node v ₂:

We observe that v ₂ = 0 (virtual ground).

Collecting like terms and rearranging (1.83) and (1.84) we get

and

Differentiation of (1.86) yields

and by substitution of given numerical values into (1.85) through (1.87), we get

or

Next, substitution of (1.89) and (1.90) into (1.88) yields

or

Division by ? 125 10 ^?13 yields

or

We use MATLAB to find the roots of the characteristic equation of (1.92).

<span class="serif">syms s; y0=solve('s^2+2*10^3*s+2*10^6')</span>y0 =[ -1000+1000*i][ -1000-1000*i]

that is,

We cannot classify the given circuit as series or parallel and therefore, we should not use the damping ratio ? _S or ? _P. Instead, for the natural response v _n( t) we will use the...