Nineth-Order Butterworth Filter Function

*
* First-Order Butterworth Filter Function Format
*
*               w0
* TF(s) = -------------
*          aN * s + w0
*
* Second-Order Butterworth Filter Function Format
*
*                w0^2
* TF(s) = -------------------
*         s^2 + aN * s + w0^2
*

.param w0 = 67730   $ pole angular frequency
.param a1 = 1       $ s-multiplier a constant 1
.param a2 = 1.8794  $ s-multiplier a constant 2
.param a3 = 1.5321  $ s-multiplier a constant 3
.param a4 = 1       $ s-multiplier a constant 4
.param a5 = 0.3472  $ s-multiplier a constant 5

** Circuit Description **
* input signal
Vin 1 0 AC 1V
* a cascade of biquads forming a 9th-order Butterworth Filter Function
* first biquad
R1 1 0 100Meg
* E1 2 0 Laplace {V(1)} = { (6.773e+4)/(s+6.773e+4) }
AE1 1 2 filter1
.model filter1 s_xfer(gain=1
+                       num_coeff=[w0]
+                       den_coeff=[a1 w0]
+                       int_ic=[0 0])
* 2nd biquad
R2 2 0 100Meg
* E2 3 0 Laplace {V(2)} = { (6.773e+4*6.773e+4)/(s*s+1.8794*6.773e4*s+6.773e4*6.773e4) }
AE2 2 3 filter2
.model filter2 s_xfer(gain=1
+                       num_coeff=[w0^2]
+                       den_coeff=[1 {a2 * w0} w0^2]
+                       int_ic=[0 0]
* 3rd biquad
R3 3 0 100Meg
* E3 4 0 Laplace {V(3)} = { (6.773e+4*6.773e+4)/(s*s+1.5321*6.773e4*s+6.773e4*6.773e4) }
AE3 3 4 filter3
.model filter3 s_xfer(gain=1
+                       num_coeff=[w0^2]
+                       den_coeff=[1 {a3 * w0} w0^2]
+                       int_ic=[0 0] 
* 4th biquad
R4 4 0 100Meg
* E4 5 0 Laplace {V(4)} = { (6.773e+4*6.773e+4)/(s*s+1.0*6.773e4*s+6.773e4*6.773e4) }
AE4 4 5 filter4
.model filter4 s_xfer(gain=1
+                       num_coeff=[w0^2]
+                       den_coeff=[1 {a4 * w0} w0^2]
+                       int_ic=[0 0]
* 5th biquad
R5 5 0 100Meg
* E5 6 0 Laplace {V(5)} = { (6.773e+4*6.773e+4)/(s*s+0.3472*6.773e4*s+6.773e4*6.773e4) }
AE5 5 6 filter5
.model filter5 s_xfer(gain=1
+                       num_coeff=[w0^2]
+                       den_coeff=[1 {a5 * w0} w0^2]
+                       int_ic=[0 0]
* output
Rout 6 0 1k
** Analysis Requests **
.AC LIN 100 1Hz 20kHz
** Output Requests **
.PLOT AC VdB(6) cph(v(6))
.probe
.end