Just a filter

.symbolic gain matrix

(\begin{matrix} 0 \\ 0 \\ 0 \\ V_{s} \\ 0 \\ 0 \\ 0 \end{matrix}) = (\begin{matrix} C_{a} s & - C_{a} s & 0 & 1 & 1 & 0 & 0 \\ - C_{a} s & \frac{1}{R_{L}} + 3 C_{a} s & - \frac{1}{R_{L}} - 2 C_{a} s & 0 & 0 & 1 & 1 \\ 0 & - \frac{1}{R_{L}} - 2 C_{a} s & \frac{1}{R_{L}} + 3 C_{a} s & 0 & - 1 & 0 & - 1 \\ 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 1 & 0 & - 1 & 0 & - L_{a} s & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & - L_{a} s & 0 \\ 0 & 1 & - 1 & 0 & 0 & 0 & - 2 L_{a} s \end{matrix}) (\begin{matrix} V_{1} \\ V_{2} \\ V_{3} \\ I_{V_{i n}} \\ I_{L_{1}} \\ I_{L_{2}} \\ I_{L_{3}} \end{matrix})

.symbolic gain fourier

\frac{V_{2} - V_{3}}{V_{i n}} = - \frac{1.0 (4.0 C_{a} L_{a} π^{2} R_{L} f^{2} + R_{L})}{- 20.0 C_{a} L_{a} π^{2} R_{L} f^{2} + π L_{a} f 4.0 i + 2.0 R_{L}}

.numeric gain pz

The zero-frequency value of GAIN = -0.5 [-].

Poles of GAIN; units HZ.


Poles	Real part	Imaginary part	Magnitude	Q

$1$	$- 31.83 \times 1 0^{3}$	$3.183 \times 1 0^{6}$	$3.183 \times 1 0^{6}$	$50.0$
$2$	$- 31.83 \times 1 0^{3}$	$- 3.183 \times 1 0^{6}$	$3.183 \times 1 0^{6}$	$50.0$

Zeros of GAIN; units HZ.


Zeros	Real part	Imaginary part	Magnitude	Q

$1$	$- 5.033 \times 1 0^{6}$	$0$	$5.033 \times 1 0^{6}$	$-$
$2$	$5.033 \times 1 0^{6}$	$0$	$5.033 \times 1 0^{6}$	$-$

.plot gain pz

Figure 1:

slicap-gain-pz.png

.plot gain step .t 0 1.5u

Figure 2:

slicap-gain-step-_t-0-1_5u.png

About

LATEX generated by SLiCAP (Symbolic Linear Circuit Analysis Program): a MuPAD application. SLiCAP �2008-2009, Montagne Design & Consultancy, Delft, The Netherlands. MuPAD Pro 4.0.6. ’The Open Computer Algebra System’ �1997-2008, is a product of SciFace Software. May 18, 2009, total SLiCAP version 3.1 processing time: 4.35 seconds (limit=600 seconds).