Mark stable point of tank plotting with hard gain limit

TankGlobals.py

@@ -5,21 +5,22 @@ import numpy as np
 # Operating Enviornment
 #####
 f0		= 28
-bw0		= 6.5 # assumed tuning range (GHz)
-bw_plt	= 3 # Plotting range (GHz)
+bw0		= 8 # assumed tuning range (GHz)
+bw_plt	= 4 # Plotting range (GHz)
 fbw		= bw0/f0 # fractional bandwidth
 
 frequency_sweep_steps = 101
-gamma_sweep_steps = 16
+gamma_sweep_steps = 8
 
 gamma = 1 - np.power(f0 / (f0 + bw0/2),2)
 gamma_limit_ratio = 0.99 # how close gamma can get to theoretical extreme
+phase_limit_requested = (1-1/gamma_sweep_steps)*np.pi/2
 
 # Configuration Of Hardware
 #####
-q1_L	= 10
-q1_C	= 10
-l1		= 100e-3 # nH
+q1_L	= 20
+q1_C	= 7
+l1		= 180e-3 # nH
 gm1		= 25e-3 # S
 
 # Compute frequency sweep
@@ -44,6 +45,6 @@ g1		= g1_L + g1_C
 gamma_max = g1 * np.sqrt(l1/c1)
 if gamma > (gamma_limit_ratio * gamma_max):
 	print("==> WARN: Gamma to large, reset to %.3f (was %.3f) <==" % \
-		(gamma_max_cap*gamma_max, gamma))
-	gamma = gamma_max_cap*gamma_max
+		(gamma_limit_ratio * gamma_max, gamma))
+	gamma = gamma_limit_ratio * gamma_max
 

tankPlot.py

@@ -32,7 +32,7 @@ def atan(x):
 ################################################################################
 # Override the defaults for this script
 rcParams['figure.figsize'] = [10,7]
-default_window_position='+20+80'
+default_window_position=['+20+80', '+120+80']
 
 ################################################################################
 # Operating Enviornment (i.e. circuit parameters)
@@ -50,6 +50,15 @@ g1_limit = np.sqrt( g1*g1 - (gamma*gamma) * c1/l1  )
 K_limit = np.sqrt(c1/l1)*1/g1_limit
 phase_limit = np.mod(np.pi/2 - np.arctan( -1/K_limit * 1/gamma ),np.pi) - np.pi
 
+if abs(phase_limit) < phase_limit_requested:
+	print("==> WARN: Phase Beyond bounds, leaving at limits. <==")
+	print("==> %.3f requested, but hardware limit is %.3f <==" % \
+		(180/np.pi*phase_limit_requested, 180/np.pi*abs(phase_limit)))
+	sys.exit(-1)
+else:
+	phase_limit = phase_limit_requested
+
+
 # This gives us our equal phase spacing points
 phase_swp = np.linspace(-1,1,gamma_sweep_steps) * phase_limit
 # Then use this to compute the gamma steps to produce arbitrary phase given
@@ -85,9 +94,14 @@ for itune,gamma_tune in enumerate(gamma_swp):
 	tf[itune,:] = tf_tmp
 
 tf = tf.T
-tf_d = tf[:,1:]-tf[:,:-1]
-tf_r = tf / (tf[:,int(tf.shape[1]/2)]*np.ones((tf.shape[1],1))).T
+# double to describe with perfect inversion stage
+tf = np.column_stack((tf,-tf))
+
+ref_index = int(gamma_swp.shape[0]/2)
+tf_r = tf / (tf[:,ref_index]*np.ones((tf.shape[1],1))).T
 y_tank = y_tank.T
+
+print(ang(tf[f==28,:]))
 ################################################################################
 
 h1 = pp.figure()
@@ -102,7 +116,7 @@ ax4 = h1.add_subplot(2,2,4)
 ax1.plot(y_tank, datatype=SmithAxes.Y_PARAMETER, marker="None")
 ax2.plot(np.angle(tf), dB20(tf))
 ax3.plot(f,dB20(tf))
-ax4.plot(f,ang(tf))
+ax4.plot(f,ang_unwrap(tf))
 
 ################################################################################
 ax8 = h2.add_subplot(2,1,1)
@@ -130,7 +144,7 @@ for ax_T in [ax3, ax4, ax8, ax9]:
 ################################################################################
 h1.tight_layout()
 h2.tight_layout()
-mgr.window.geometry(default_window_position)
+mgr.window.geometry(default_window_position[0])
 h1.show()
-mgr.window.geometry(default_window_position)
+mgr.window.geometry(default_window_position[1])
 h2.show()

tankPlot_v1.py

@@ -0,0 +1,150 @@
+#!/usr/bin/env python3
+
+import numpy as np
+
+from matplotlib import rcParams, pyplot as pp
+import LPRDefaultPlotting
+
+import sys
+sys.path.append("./pySmithPlot")
+import smithplot
+from smithplot import SmithAxes
+
+################################################################################
+# Define my helper functions.
+def dB20(volt_tf):
+	"""Describe signal gain of a transfer function in dB (i.e. 20log(x))"""
+	return 20*np.log10(np.abs(volt_tf))
+def ang(volt_tf):
+	"""Describe phase of a transfer function in degrees. Not unwrapped."""
+	return 180/np.pi*np.angle(volt_tf)
+def ang_unwrap(volt_tf):
+	"""Describe phase of a transfer function in degrees. With unwrapping."""
+	return 180/np.pi*np.unwrap(np.angle(volt_tf))
+def dB10(pwr_tf):
+	"""Describe power gain of a transfer function in dB (i.e. 10log(x))"""
+	return 10*np.log10(np.abs(pwr_tf))
+	
+def atan(x):
+	return 180/np.pi*np.arctan(x)
+
+
+################################################################################
+# Override the defaults for this script
+rcParams['figure.figsize'] = [10,7]
+default_window_position=['+20+80', '+120+80']
+
+################################################################################
+# Operating Enviornment (i.e. circuit parameters)
+from TankGlobals import *
+
+################################################################################
+# Now generate the sweep of resonance tuning (gamma, and capacitance)
+
+# Linear based gamma spacing
+#gamma_swp = np.linspace(-gamma,gamma,gamma_sweep_steps)
+
+# Linear PHASE gamma spacing
+# First compute the most extreme phase given the extreme gamma
+g1_limit = np.sqrt( g1*g1 - (gamma*gamma) * c1/l1  )
+K_limit = np.sqrt(c1/l1)*1/g1_limit
+phase_limit = np.mod(np.pi/2 - np.arctan( -1/K_limit * 1/gamma ),np.pi) - np.pi
+
+if abs(phase_limit) < phase_limit_requested:
+	print("==> WARN: Phase Beyond bounds, leaving at limits. <==")
+	print("==> %.3f requested, but hardware limit is %.3f <==" % \
+		(180/np.pi*phase_limit_requested, 180/np.pi*abs(phase_limit)))
+	sys.exit(-1)
+else:
+	phase_limit = phase_limit_requested
+
+
+# This gives us our equal phase spacing points
+phase_swp = np.linspace(-1,1,gamma_sweep_steps) * phase_limit
+# Then use this to compute the gamma steps to produce arbitrary phase given
+# our perfect gain constraint.
+gamma_swp = np.sign(phase_swp)/np.sqrt(np.power(np.tan(np.pi/2 - phase_swp),2)+1) * g1 / np.sqrt(c1/l1)
+
+# compute correction factor for g1 that will produce common gain at f0
+g1_swp = np.sqrt( g1*g1 - (gamma_swp*gamma_swp) * c1/l1  )
+# and compute how much of a negative gm this requres, and it's relative
+# proportion to the gm of the assumed main amplifier gm.
+g1_boost = (g1_swp - g1)
+g1_ratio = -g1_boost / gm1
+
+c1_swp = c1 * (1 + gamma_swp)
+
+## Report System Descrption
+print('  L1 = %.3fpH, C1 = %.3ffF' % (1e3*l1, 1e6*c1))
+print('    Rp = %.3f Ohm' % (1/g1))
+print('    Max G1 boost %.2fmS (%.1f%% of gm1)' % \
+	(1e3*np.max(np.abs(g1_boost)), 100*np.max(g1_ratio)))
+
+y_tank = np.zeros((len(gamma_swp),len(f)), dtype=complex)
+tf = np.zeros((len(gamma_swp),len(f)), dtype=complex)
+for itune,gamma_tune in enumerate(gamma_swp):
+	c1_tune = c1_swp[itune]
+	g1_tune = g1_swp[itune]
+	K = np.sqrt(c1/l1)/g1_tune
+	y_tank_tmp = g1_tune + jw*c1_tune + 1/(jw * l1)
+	y_tank[itune,:] = y_tank_tmp
+	tf_tmp = gm1 / g1_tune * \
+		1j*(1+delta) / \
+		( 1j*(1+delta) + K*(1 - (1+gamma_tune)*np.power(1+delta,2)) )
+	tf[itune,:] = tf_tmp
+
+tf = tf.T
+# double to describe with perfect inversion stage
+tf = np.column_stack((tf,-tf))
+
+ref_index = int(gamma_swp.shape[0]/2)
+tf_r = tf / (tf[:,ref_index]*np.ones((tf.shape[1],1))).T
+y_tank = y_tank.T
+
+print(ang(tf[f==28,:]))
+################################################################################
+
+h1 = pp.figure()
+h2 = pp.figure(figsize=(5,7))
+mgr = pp.get_current_fig_manager()
+################################################################################
+ax1 = h1.add_subplot(2,2,1, projection='smith')
+ax2 = h1.add_subplot(2,2,3, projection='polar')
+ax3 = h1.add_subplot(2,2,2)
+ax4 = h1.add_subplot(2,2,4)
+
+ax1.plot(y_tank, datatype=SmithAxes.Y_PARAMETER, marker="None")
+ax2.plot(np.angle(tf), dB20(tf))
+ax3.plot(f,dB20(tf))
+ax4.plot(f,ang_unwrap(tf))
+
+################################################################################
+ax8 = h2.add_subplot(2,1,1)
+ax9 = h2.add_subplot(2,1,2)
+ax8.plot(f,dB20(tf_r))
+ax9.plot(f,ang_unwrap(tf_r.T).T)
+
+ax1.set_title('Tank Impedance')
+ax2.set_title('Transfer Function')
+
+ax3.set_title('TF Gain')
+ax3.set_ylabel('Gain (dB)')
+ax4.set_title('TF Phase')
+ax4.set_ylabel('Phase (deg)')
+ax8.set_title('TF Relative Gain')
+ax8.set_ylabel('Relative Gain (dB)')
+ax9.set_title('TF Relative Phase')
+ax9.set_ylabel('Relative Phase (deg)')
+for ax_T in [ax3, ax4, ax8, ax9]:
+	ax_T.grid()
+	ax_T.set_xlabel('Freq (GHz)')
+	ax_T.set_xlim(( np.min(f), np.max(f) ))
+
+
+################################################################################
+h1.tight_layout()
+h2.tight_layout()
+mgr.window.geometry(default_window_position[0])
+h1.show()
+mgr.window.geometry(default_window_position[1])
+h2.show()