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* ============================================================================
* 6th-Order Continuous-Time Active-RC Biquad Cascade for DFF Operator
* Fractional order m = 0.5, Beta = 2.35, Alpha = 0.14
* Time-scaling constant T (seconds) maps normalized s to physical frequency
* Compatible with SPICE-Online (ngspice-based engine)
* ============================================================================

.param m = 0.5
.param beta = 2.35
.param alpha = 0.14
.param T = 1          ; Time-scaling constant (s); set T = 1/omega_c

* --- Coefficient Calculation ---
.param a0 = {m^2 + (beta + 1)*m + beta}
.param a2 = {m^2 - (beta + 1)*m + beta}
.param k_fac = {1 + alpha * sin(m*pi)}
.param a1_mod = {k_fac * 2 * m * (beta + 1) * tan((2 - m)*pi/4)}

* --- Base Component Values ---
.param R_base = 10k
.param C_base = {1n * T}

* ============================================================================
* Input AC Source (Required for AC Analysis)
* ============================================================================
Vin In 0 AC 1

* ============================================================================
* Biquad Stage 1 (In -> Out1)
* ============================================================================
E_OP1 N001 0 N002 0 1e5
R1_1 In N002 {a2*R_base}
C1_1 N002 N001 {a0*C_base}
R2_1 N001 N002 {a1_mod*R_base}
EBUF1 Out1 0 N001 0 1

* ============================================================================
* Biquad Stage 2 (Out1 -> Out2)
* ============================================================================
E_OP2 N003 0 N004 0 1e5
R1_2 Out1 N004 {a2*R_base}
C1_2 N004 N003 {a0*C_base}
R2_2 N003 N004 {a1_mod*R_base}
EBUF2 Out2 0 N003 0 1

* ============================================================================
* Biquad Stage 3 (Out2 -> Out3)
* ============================================================================
E_OP3 N005 0 N006 0 1e5
R1_3 Out2 N006 {a2*R_base}
C1_3 N006 N005 {a0*C_base}
R2_3 N005 N006 {a1_mod*R_base}
EBUF3 Out3 0 N005 0 1

* ============================================================================
* Biquad Stage 4 (Out3 -> Out4)
* ============================================================================
E_OP4 N007 0 N008 0 1e5
R1_4 Out3 N008 {a2*R_base}
C1_4 N008 N007 {a0*C_base}
R2_4 N007 N008 {a1_mod*R_base}
EBUF4 Out4 0 N007 0 1

* ============================================================================
* Biquad Stage 5 (Out4 -> Out5)
* ============================================================================
E_OP5 N009 0 N010 0 1e5
R1_5 Out4 N010 {a2*R_base}
C1_5 N010 N009 {a0*C_base}
R2_5 N009 N010 {a1_mod*R_base}
EBUF5 Out5 0 N009 0 1

* ============================================================================
* Biquad Stage 6 (Out5 -> Out)
* ============================================================================
E_OP6 N011 0 N012 0 1e5
R1_6 Out5 N012 {a2*R_base}
C1_6 N012 N011 {a0*C_base}
R2_6 N011 N012 {a1_mod*R_base}
EBUF6 Out 0 N011 0 1

* ============================================================================
* AC Analysis: 4 decades (0.01 to 100 rad/s -> 1.59 mHz to 15.9 Hz)
* ============================================================================
.ac dec 100 0.00159 15.9

* Output: Magnitude (dB) and Phase (degrees) of final stage
.plot ac dB(V(Out)) VP(Out)

.end