Add script for computing controlled-root parameters

peregrine/include/controlled_root.py

@@ -0,0 +1,112 @@
+# -*- coding: utf-8 -*-
+"""
+Created on Thu Jul 14 14:29:34 2016
+
+@author: tpaakki
+
+This script generates controlled-root loop parameters, based on 
+"Stephens, S. A., and J. C. Thomas, "Controlled-Root Formulation for 
+Digital Phase-Locked Loops," IEEE Trans. on Aerospace and Electronics
+ Systems, January 1995"
+
+"""
+from math import factorial, exp
+import cmath
+
+def controlled_root(N, T, BW):
+  # Input Parameters
+  # N [-]  Loop Order
+  # T [s]  Integration Time
+  # BW [Hz] Loop Bandwidth
+  # Output Parameters
+  # K [-] Loop constants
+
+  K = []
+  tol = 1.e-6     # Error tolerance
+  goal = BW*T     # This is the BLT we want to solve
+
+  # Few precomputed factorial parameters
+  if N > 1:
+    fac1 = factorial(N)/(factorial(1)*factorial(N-1))     # eq.(45)
+  if N > 2:
+    fac2 = factorial(N)/(factorial(2)*factorial(N-2))     # eq.(46)
+    fac3 = factorial(N-1)/(factorial(1)*factorial(N-1-1)) # eq.(46)
+    fac4 = factorial(N-2)/(factorial(1)*factorial(N-2-1)) # eq.(46)
+
+  beta = 0.5
+  step = 0.25
+  done = True
+  ii = 1
+  if N == 1:
+    while done:
+      z1 = exp(-beta)        # eq.(50)
+      K1 = 1.-z1             # eq.(49)
+      blt = K1/(2.*(2.-K1))  # Table IV
+      err = goal-blt
+      if abs(err) <= tol:
+        K = [K1]
+        done = False
+      if err > 0.:
+        beta = beta + step
+        step = step / 2.
+      if err < 0.:
+        beta = beta - step
+        step = step / 2.
+      if ii > 30:
+        'Error - did not converge'
+        done = False
+      ii = ii + 1;
+  if N == 2:
+    while done:
+      z1 = cmath.exp(-beta*(1.+1.j)) # eq.(50)
+      z2 = cmath.exp(-beta*(1.-1.j)) # eq.(50)
+      K1 = 1.-z1*z2                  # eq.(49)
+      K1 = K1.real
+      K2 = fac1-K1-z1-z2             # eq.(45)
+      K2 = K2.real
+      blt = (2.*K1*K1+2.*K2+K1*K2)/(2.*K1*(4.-2*K1-K2)) # Table IV
+      err = goal-blt
+      if abs(err) <= tol:
+        K = K1, K2
+        done = False
+      if err > 0.:
+        beta = beta + step
+        step = step / 2.
+      if err < 0.:
+        beta = beta - step
+        step = step / 2.
+      if ii > 30:
+        'Error - did not converge'
+        done = False
+        ii = ii + 1;
+  if N == 3:
+    while done:
+      z1 = exp(-beta)                # eq.(50)
+      z2 = cmath.exp(-beta*(1.+1.j)) # eq.(50)
+      z3 = cmath.exp(-beta*(1.-1.j)) # eq.(50)
+      K1 = 1-z1*z2*z3                # eq.(49)
+      K1 = K1.real
+      summ = z1*z2+z1*z3+z2*z3;
+      K2 = (fac2-fac3*K1-summ)/fac4  # eq.(46)
+      K2 = K2.real
+      K3 = fac1-K1-K2-z1-z2-z3       # eq.(45)
+      K3 = K3.real
+      blt = (4.*K1*K1*K2-4.*K1*K3+4.*K2*K2+2.*K1*K2*K2+4.*K1*K1*K3+4.*K2*K3
+           +3*K1*K2*K3+K3*K3+K1*K3*K3)/(2.*(K1*K2-K3+K1*K3)*(8.
+           -4.*K1-2.*K2-K3))         # Table IV
+      err = goal-blt
+      if abs(err) <= tol:
+        K = K1, K2, K3
+        done = False
+      if err > 0.:
+        beta = beta + step
+        step = step / 2.
+      if err < 0.:
+        beta = beta - step
+        step = step / 2.
+      if ii > 30:
+        'Error - did not converge'
+        done = False
+      ii = ii + 1;
+
+  return K