Blame view

SRC/NETWORK_SYNTHESIS/include_minimum_resistance_function.F90 11.3 KB
189467e4   Steve Greedy   First Public Release
1
!
fe64b32b   Chris Smartt   Update file heade...
2
! This file is part of SACAMOS, State of the Art CAble MOdels for Spice. 
189467e4   Steve Greedy   First Public Release
3
4
5
! It was developed by the University of Nottingham and the Netherlands Aerospace 
! Centre (NLR) for ESA under contract number 4000112765/14/NL/HK.
! 
fe64b32b   Chris Smartt   Update file heade...
6
! Copyright (C) 2016-2018 University of Nottingham
189467e4   Steve Greedy   First Public Release
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
! 
! SACAMOS is free software: you can redistribute it and/or modify it under the 
! terms of the GNU General Public License as published by the Free Software 
! Foundation, either version 3 of the License, or (at your option) any later 
! version.
! 
! SACAMOS is distributed in the hope that it will be useful, but 
! WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY 
! or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License 
! for more details.
! 
! A copy of the GNU General Public License version 3 can be found in the 
! file GNU_GPL_v3 in the root or at <http://www.gnu.org/licenses/>.
! 
! SACAMOS uses the EISPACK library (in /SRC/EISPACK). EISPACK is subject to 
! the GNU Lesser General Public License. A copy of the GNU Lesser General Public 
! License version can be found in the file GNU_LGPL in the root of EISPACK 
! (/SRC/EISPACK ) or at <http://www.gnu.org/licenses/>.
! 
! The University of Nottingham can be contacted at: ggiemr@nottingham.ac.uk
!
fe64b32b   Chris Smartt   Update file heade...
28
!
189467e4   Steve Greedy   First Public Release
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
! File Contents:
! SUBROUTINE calculate_min_resistance_function(H,R,w0)
! SUBROUTINE calculate_min_resistance_value(H,R,w0)
!
! NAME
!     calculate_min_resistance_value
!
! DESCRIPTION
!     This subroutine calculates the minimum resistance of a rational transfer function
!     and the angular frequency at which it occurs
!     See F. F. Kuo, "Network Analysis and Synthesis" section 10.3
!
!     The algorithm first obtains an expression for the real part of the rational function as
!     a function of frequency. This is then differentiated and the minima calculated.
!     The lowest minimum, or the resistance as f-> infinty if is smaller is then the minimum resistance
!
! SEE ALSO
!
!
! HISTORY
!
!     started 05/10/2017 CJS
!
  SUBROUTINE calculate_min_resistance_value(H,R,w0)

USE type_specifications
USE general_module
USE constants
USE frequency_spec
USE filter_module
USE Sfilter_fit_module

IMPLICIT NONE

! variables passed to subroutine  
  type(Sfilter),intent(INOUT)       :: H        ! Input Rational transfer function 
  real(dp),intent(OUT)              :: R        ! Output Minimum resistance (real part of the transfer function)
  real(dp),intent(OUT)              :: w0       ! Output Angular frequency at which the minimum occurs
  
! local variables

  type(Sfilter)    :: Hnew
  type(polynomial) :: m1,m2,n1,n2,t1,t2,A2,A,Ap,B,B2,Bp,Q
  integer  :: i,ii,order,m_order,n_order,a_order
  
  integer      :: poly_order
  complex(dp),allocatable :: roots(:)
  complex(dp),allocatable :: rroots(:)
  complex(dp),allocatable :: croots(:)
  integer                 :: nreal
  integer                 :: ncomplex
  
  integer  :: root
  real(dp) :: min_R,min_w0,w,f,R_w
  
  logical :: pole_at_zero
  logical :: local_verbose

    
!START

!  local_verbose=.TRUE.
  local_verbose=.FALSE.

  if (local_verbose) then
    write(*,*)'CALLED calculate_min_resistance_value'
    write(*,*)'Input filter function:'
    CALL write_Sfilter(H,0)
  end if
  
  if (abs(H%b%coeff(0)).LT.zero_test_small) then
    pole_at_zero=.TRUE.
  else
    pole_at_zero=.FALSE.
  end if
  
! assemble the odd and even polynomials m1 and n1 from the numerator of H 

  order=H%a%order
  if (mod(order,2).EQ.0) then
    m_order=order
    n_order=max(order-1,0)
  else
    m_order=max(order-1,0)
    n_order=order 
  end if
  
  m1=allocate_polynomial(m_order)
  n1=allocate_polynomial(n_order)
  
  m1%coeff(:)=0d0
  do i=0,m_order,2
    m1%coeff(i)=H%a%coeff(i)
  end do
  
  n1%coeff(:)=0d0
  do i=1,n_order,2
    n1%coeff(i)=H%a%coeff(i)
  end do
  
  if (local_verbose) then
    write(*,*)'Numerator:'
    CALL write_poly_local3(H%a)  
    write(*,*)'m1: even order terms'
    CALL write_poly_local3(m1)  
    write(*,*)'n1: odd order terms'
    CALL write_poly_local3(n1)  
  end if

! assemble the odd and even polynomials m2 and n2 from the denominator of H 

  order=H%b%order
  if (mod(order,2).EQ.0) then
    m_order=order
    n_order=max(order-1,0)
  else
    m_order=max(order-1,0)
    n_order=order 
  end if
  
  m2=allocate_polynomial(m_order)
  n2=allocate_polynomial(n_order)
  
  m2%coeff(:)=0d0
  do i=0,m_order,2
    m2%coeff(i)=H%b%coeff(i)
  end do
  
  n2%coeff(:)=0d0
  do i=1,n_order,2
    n2%coeff(i)=H%b%coeff(i)
  end do
  
  if (local_verbose) then
    write(*,*)'Denominator:'
    CALL write_poly_local3(H%b)  
    write(*,*)'m2: even order terms'
    CALL write_poly_local3(m2)  
    write(*,*)'n2: odd order terms'
    CALL write_poly_local3(n2)  
  end if

! Calculate the polynomial A2(jw)=m1(jw)m2(jw)-n1(jw)n2(jw)

  t1=m1*m2
  t2=n1*n2
  A2=t1-t2
  
  CALL get_min_order_poly(A2)
  
  if (local_verbose) then
    write(*,*)'A2(jw)=m1m2-n1n2'
    CALL write_poly_local3(A2)  
   end if
   
! Calculate the coefficients of A(w)

  order=A2%order
  if (mod(order,2).EQ.0) then
    a_order=order
  else
    write(*,*)'Error in calculate_min_resistance_function. Order of A2(jw) is not an even number'
  end if
  
  A=allocate_polynomial(a_order)
  
  do i=0,a_order
    A%coeff(i)=A2%coeff(i)
  end do

! At the moment A is a function of (jw) not w with zero odd order coefficients
! We get the function of w by making the jw**2n order coefficients negative
  do i=2,a_order,4
    A%coeff(i)=-A%coeff(i)
  end do
    
  CALL get_min_order_poly(A)
  
  if (local_verbose) then
    write(*,*)'A(w)='
    CALL write_poly_local3(A)  
   end if

! Calculate the polynomial B2(jw)=m2(jw)m2(jw)-n2(jw)n2(jw)

  t1=m2*m2
  t2=n2*n2
  B2=t1-t2
  
  CALL get_min_order_poly(B2)
  
  if (local_verbose) then
    write(*,*)'B2(jw)=m1m2-n1n2'
    CALL write_poly_local3(B2)  
   end if
   
! Calculate the coefficients of B(w)

  order=B2%order
  if (mod(order,2).EQ.0) then
    a_order=order
  else
    write(*,*)'Error in calculate_min_resistance_function. Order of B2(jw) is not an even number'
  end if
  
  B=allocate_polynomial(a_order)
  
  do i=0,a_order
    B%coeff(i)=B2%coeff(i)
  end do

! Bt the moment B is a function of (jw) not w with zero odd order coefficients
! We get the function of w by making the jw**2n order coefficients negative
  do i=2,a_order,4
    B%coeff(i)=-B%coeff(i)
  end do
    
  CALL get_min_order_poly(B)
  
  if (local_verbose) then
    write(*,*)'B(w)='
    CALL write_poly_local3(B)  
   end if

! Calculate the derivative of A(w)/B(w) wrt w

  order=max(0,A%order-1)
  Ap=allocate_polynomial(order)
  
  if (A%order.GT.0) then
    do i=0,Ap%order
      Ap%coeff(i)=A%coeff(i+1)*dble(i+1)
    end do
  end if
  
  if (local_verbose) then
    write(*,*)"Deivative function A'(w)="
    CALL write_poly_local3(Ap)  
   end if

  order=max(0,B%order-1)
  Bp=allocate_polynomial(order)

  if (B%order.GT.0) then
    do i=0,Bp%order
      Bp%coeff(i)=B%coeff(i+1)*dble(i+1)
    end do
  end if
  
  if (local_verbose) then
    write(*,*)"Deivative function B'(w)="
    CALL write_poly_local3(Bp)  
   end if
  
! Calculate the zeros of the derivative function d/dw(A(w)/B(w))=
  t1=Ap*B
  t2=A*Bp
  Q=t1-t2
   
  if (local_verbose) then
    write(*,*)"we require Q(w)=0 where Q="
    CALL write_poly_local3(Q)  
   end if
 
  CALL get_min_order_poly(Q)
  
  if (local_verbose) then
    write(*,*)"we require Q(w)=0 where Q="
    CALL write_poly_local3(Q)  
   end if

  poly_order=Q%order
  ALLOCATE( roots(1:poly_order) )
  CALL findroots(Q,roots,poly_order)
  
  if (local_verbose) then
    write(*,*)'Roots of the derivative function are'
    do root=1,poly_order
      write(*,*)roots(root)
    end do
  end if
  
  ALLOCATE( rroots(1:poly_order) )
  ALLOCATE( croots(1:poly_order) )
  CALL rootsort(poly_order,roots,rroots,             &
                croots,nreal,ncomplex,poly_order)
                     
  if (local_verbose) write(*,*)'Getting the high frequency resistance' 
  
  
  write(*,*)'Getting the high frequency resistance of H:' 
  CALL write_Sfilter(H,0)
  write(*,*)'aorder=',H%a%order
  write(*,*)'border=',H%b%order
  
  min_w0=1D30
  min_R=evaluate_Sfilter_high_frequency_limit(H)
  if (local_verbose) write(*,*)'High frequency resistance=',min_R 
  
  if (local_verbose) write(*,*)'Checking real roots: number of roots=',nreal,poly_order 
  do root=1,nreal
    
    w=-dble(rroots(root))
    f=w*H%wnorm/(2d0*pi)  
    
    if ((pole_at_zero).AND.(abs(f).LT.zero_test_small)) then
! perturb the frequency slightly away from the pole at zero
      write(*,*)'Special case, f=',f
      write(*,*)'(pole_at_zero).AND.(abs(f).LT.zero_test_small),zero_test_small=',zero_test_small
      f=f+zero_test_small
      write(*,*)'new f=',f
    end if

    R_w=evaluate_Sfilter_frequency_response(H,f)
    
    if (local_verbose) then
      write(*,*)'root',rroots(root),'w=',w,' R=',R_w
    end if
   
    if (R_w.EQ.min_R) then
! if we have roots at + and - p, choose the one with positive frequency
      min_R=R_w
      min_w0=max(w,min_w0)
    else if (R_w.LT.min_R) then
      min_R=R_w
      min_w0=w
    end if
    
  end do
  
  R=min_R
  w0=min_w0

  if (local_verbose) then
    write(*,*)'FINISHED calculate_min_resistance_value'
    write(*,*)
    write(*,*)'R0=',R
    write(*,*)'w0=',w0
    write(*,*)
  end if
  
! finish up
  
  DEALLOCATE( roots )
  DEALLOCATE( rroots )
  DEALLOCATE( croots )

  RETURN
  END SUBROUTINE calculate_min_resistance_value
!
! NAME
!     calculate_min_resistance_function
!
! DESCRIPTION
!     This subroutine calculates the minimum resistance value of a PR function
!     and then subtracts it from the input function to give a function
!     whose minimum resistance is zero. This is required in the Brune Synthesis. 
!
! SEE ALSO
!
!
! HISTORY
!
!     started 04/03/09 CJS
!
  SUBROUTINE calculate_min_resistance_function(H,R,w0)

USE type_specifications
USE general_module
USE constants
USE frequency_spec
USE filter_module
USE Sfilter_fit_module

IMPLICIT NONE

! variables passed to subroutine  
  type(Sfilter),intent(INOUT)    :: H            ! Input/ Output Rational transfer function 
  real(dp),intent(OUT)           :: R            ! Output Minimum resistance (real part of the transfer function)
  real(dp),intent(OUT)           :: w0           ! Output Angular frequency at which the minimum occurs
  
! local variables

  type(Sfilter)    :: Hnew
  type(polynomial) :: t1,t2
  real(dp) :: min_R,min_w0,w,f,R_w
  
  logical ::local_verbose

    
!START

  local_verbose=.TRUE.

  if (local_verbose) then
    write(*,*)'CALLED calculate_min_resistance_function'
    write(*,*)'Input filter function:'
    CALL write_Sfilter(H,0)
  end if
  
  CALL calculate_min_resistance_value(H,min_R,min_w0)

! Deal with the numerics around small values of min_R
  if (min_R.LT.-zero_test_small) then
    write(*,*)'calculate_min_resistance_function called with non positive real function'
    STOP
  else if (abs(min_R).LT.zero_test_small) then
    min_R=0d0
  end if
  
  if (local_verbose) then
    write(*,*)'Minimum R=',min_R,' at w=',min_w0 
  end if
  
! now subtract R_min from the input function H(jw)

  Hnew=H
  
  t1=H%a
  t2=H%b
  t2%coeff(:)=t2%coeff(:)*min_R
  
  Hnew%a=t1-t2
  CALL get_min_order_poly(Hnew%a)
  
  H=Hnew
  
  R=min_R
  w0=min_w0

  if (local_verbose) then
    write(*,*)'FINISHED calculate_min_resistance_function'
    write(*,*)'Output filter function:'
    CALL write_Sfilter(H,0)
    write(*,*)
  end if

  RETURN
  END SUBROUTINE calculate_min_resistance_function