In [2]:
Copied!
import matplotlib.pyplot as plt
import numpy as np
def denom(w, wn, Q):
zeta = wn/Q
return wn*wn + 1j*w*zeta - w*w
def Hlp(w, wn, Q):
return wn*wn / denom(w, wn, Q)
def Hhp(w, wn, Q):
return -w*w / denom(w, wn, Q)
def Hbp(w, wn, Q):
zeta = wn/Q
return 1j*w*zeta / denom(w, wn, Q)
f = np.logspace(-1,3,401)
w = 2*np.pi*f
fn = 10
wn = 2*np.pi*fn
Q = 3 # 1/np.sqrt(2)
filters = [{'label':'low-pass', 'H':Hlp(w,wn,Q)},
{'label':'high-pass', 'H':Hhp(w,wn,Q)},
{'label':'band-pass', 'H':Hbp(w,wn,Q)},
{'label':'band-stop', 'H':Hlp(w,wn,Q) + Hhp(w,wn,Q)}]
fig = plt.figure(figsize=(10, 8))
for ndx, filter in enumerate(filters):
# subplot indices are 1-based, so add 1 to ndx
ax = fig.add_subplot(2, 2, ndx+1)
fig.subplots_adjust(hspace=0.4, wspace=0.6)
Hf = filter['H']
Hmax = np.ceil(np.max(np.abs(Hf)))
angleHdeg = np.angle(Hf)*180/np.pi
amin = np.round(np.min(angleHdeg/90.))*90.
amax = np.round(np.max(angleHdeg/90.))*90.
lns1 = ax.semilogx(f, np.abs(Hf), color='c', label='magnitude')
ax.set_xlabel("f (Hz)")
ax.set_ylabel("|H|")
# ax.tick_params(axis='y')
ax.set_ylim([0, Hmax])
ax.grid(True, which='both', ls='--', alpha=0.4)
ax2 = ax.twinx()
lns2 = ax2.semilogx(f, angleHdeg, color='tab:orange', label='angle')
ax2.set_ylabel("angle(H) (deg)")
ax2.set_ylim([amin,amax])
ax2.set_yticks(np.linspace(amin,amax,int(np.round((amax-amin)/45.))+1))
# ax2.tick_params(axis='y')
# combined legend
lines = lns1 + lns2
labels = [l.get_label() for l in lines]
ax.legend(lines, labels, loc='best')
plt.title(f"2nd order {filter['label']} filter, Q={Q:1.3f}")
plt.show()
import matplotlib.pyplot as plt
import numpy as np
def denom(w, wn, Q):
zeta = wn/Q
return wn*wn + 1j*w*zeta - w*w
def Hlp(w, wn, Q):
return wn*wn / denom(w, wn, Q)
def Hhp(w, wn, Q):
return -w*w / denom(w, wn, Q)
def Hbp(w, wn, Q):
zeta = wn/Q
return 1j*w*zeta / denom(w, wn, Q)
f = np.logspace(-1,3,401)
w = 2*np.pi*f
fn = 10
wn = 2*np.pi*fn
Q = 3 # 1/np.sqrt(2)
filters = [{'label':'low-pass', 'H':Hlp(w,wn,Q)},
{'label':'high-pass', 'H':Hhp(w,wn,Q)},
{'label':'band-pass', 'H':Hbp(w,wn,Q)},
{'label':'band-stop', 'H':Hlp(w,wn,Q) + Hhp(w,wn,Q)}]
fig = plt.figure(figsize=(10, 8))
for ndx, filter in enumerate(filters):
# subplot indices are 1-based, so add 1 to ndx
ax = fig.add_subplot(2, 2, ndx+1)
fig.subplots_adjust(hspace=0.4, wspace=0.6)
Hf = filter['H']
Hmax = np.ceil(np.max(np.abs(Hf)))
angleHdeg = np.angle(Hf)*180/np.pi
amin = np.round(np.min(angleHdeg/90.))*90.
amax = np.round(np.max(angleHdeg/90.))*90.
lns1 = ax.semilogx(f, np.abs(Hf), color='c', label='magnitude')
ax.set_xlabel("f (Hz)")
ax.set_ylabel("|H|")
# ax.tick_params(axis='y')
ax.set_ylim([0, Hmax])
ax.grid(True, which='both', ls='--', alpha=0.4)
ax2 = ax.twinx()
lns2 = ax2.semilogx(f, angleHdeg, color='tab:orange', label='angle')
ax2.set_ylabel("angle(H) (deg)")
ax2.set_ylim([amin,amax])
ax2.set_yticks(np.linspace(amin,amax,int(np.round((amax-amin)/45.))+1))
# ax2.tick_params(axis='y')
# combined legend
lines = lns1 + lns2
labels = [l.get_label() for l in lines]
ax.legend(lines, labels, loc='best')
plt.title(f"2nd order {filter['label']} filter, Q={Q:1.3f}")
plt.show()
Measurement and Calibration¶
- Use the coarse adjust/cutoff and adjust the bias at the center tap of that potentiometer to 1V. Disconnect other inputs (CV and V/oct).
- Set the audio level to maximum (no attenuation).
- Apply an 8Vpp sinusoid to the audio input.
- Use the notch filter output to locate the cutoff frequency (where the AC-coupled output amplitude goes to zero and the phase inverts).
- Monitor the band pass output and adjust the resonance until you have unity gain (Q=1).
- Sweep the frequency and record the amplitudes for each filter output.
In [11]:
Copied!
# Measured 2025-12-13
vpp_in = 8
fc = 620
freq = np.array([50, 100, 200, 300, 400, 500, 600, 700, 800, 900,1000,1200,1500,2000,3000,4000,5000])
mlp = np.array([7.96,8.08,8.48,8.96,9.28,9.12,8.24,6.88,5.40,4.32,3.52,2.44,1.56,0.93,0.44,0.36,0.27])
mhp = np.array([0.22,0.36,1.04,2.28,4.08,6.16,8.00,9.04,9.36,9.44,9.28,9.12,8.80,8.48,8.20,8.12,8.08])
mbp = np.array([0.76,1.44,2.88,4.40,6.04,7.40,8.08,7.72,7.04,6.32,5.64,4.60,3.60,2.64,1.76,1.32,1.08])
mbs = np.array([8.08,8.08,7.68,6.96,5.44,3.20,0.48,2.32,4.08,5.20,6.00,6.80,7.28,7.68,7.84,7.96,8.00])
w_meas = 2*np.pi*freq
wn_meas = 2*np.pi*fc
Q_meas = 1
filters = [{'label':'low-pass', 'H':Hlp(w_meas, wn_meas, Q_meas), 'A':mlp/vpp_in},
{'label':'high-pass', 'H':Hhp(w_meas, wn_meas, Q_meas), 'A':mhp/vpp_in},
{'label':'band-pass', 'H':Hbp(w_meas, wn_meas, Q_meas), 'A':mbp/vpp_in},
{'label':'band-stop', 'H':Hlp(w_meas, wn_meas, Q_meas) + Hhp(w_meas, wn_meas, Q_meas), 'A':mbs/vpp_in}]
fig = plt.figure(figsize=(10, 8))
for ndx, filter in enumerate(filters):
# subplot indices are 1-based, so add 1 to ndx
ax = fig.add_subplot(2, 2, ndx+1)
fig.subplots_adjust(hspace=0.4, wspace=0.3)
Hf = filter['H']
Af = filter['A']
Hmax = np.ceil(np.max(np.abs(Hf)))
ln_theo = ax.semilogx(freq, np.abs(Hf), color='c', label='theory')
ln_meas = ax.semilogx(freq, Af, color='k', marker='o', linestyle='None', label='measured')
ax.set_xlabel("f (Hz)")
ax.set_ylabel("|H|")
# ax.tick_params(axis='y')
ax.set_ylim([0, Hmax])
ax.grid(True, which='both', ls='--', alpha=0.4)
# combined legend
lines = ln_theo + ln_meas
labels = [l.get_label() for l in lines]
ax.legend(lines, labels, loc='best')
plt.title(f"2nd order {filter['label']} filter, Q={Q_meas:1.1f}")
plt.show()
# Measured 2025-12-13
vpp_in = 8
fc = 620
freq = np.array([50, 100, 200, 300, 400, 500, 600, 700, 800, 900,1000,1200,1500,2000,3000,4000,5000])
mlp = np.array([7.96,8.08,8.48,8.96,9.28,9.12,8.24,6.88,5.40,4.32,3.52,2.44,1.56,0.93,0.44,0.36,0.27])
mhp = np.array([0.22,0.36,1.04,2.28,4.08,6.16,8.00,9.04,9.36,9.44,9.28,9.12,8.80,8.48,8.20,8.12,8.08])
mbp = np.array([0.76,1.44,2.88,4.40,6.04,7.40,8.08,7.72,7.04,6.32,5.64,4.60,3.60,2.64,1.76,1.32,1.08])
mbs = np.array([8.08,8.08,7.68,6.96,5.44,3.20,0.48,2.32,4.08,5.20,6.00,6.80,7.28,7.68,7.84,7.96,8.00])
w_meas = 2*np.pi*freq
wn_meas = 2*np.pi*fc
Q_meas = 1
filters = [{'label':'low-pass', 'H':Hlp(w_meas, wn_meas, Q_meas), 'A':mlp/vpp_in},
{'label':'high-pass', 'H':Hhp(w_meas, wn_meas, Q_meas), 'A':mhp/vpp_in},
{'label':'band-pass', 'H':Hbp(w_meas, wn_meas, Q_meas), 'A':mbp/vpp_in},
{'label':'band-stop', 'H':Hlp(w_meas, wn_meas, Q_meas) + Hhp(w_meas, wn_meas, Q_meas), 'A':mbs/vpp_in}]
fig = plt.figure(figsize=(10, 8))
for ndx, filter in enumerate(filters):
# subplot indices are 1-based, so add 1 to ndx
ax = fig.add_subplot(2, 2, ndx+1)
fig.subplots_adjust(hspace=0.4, wspace=0.3)
Hf = filter['H']
Af = filter['A']
Hmax = np.ceil(np.max(np.abs(Hf)))
ln_theo = ax.semilogx(freq, np.abs(Hf), color='c', label='theory')
ln_meas = ax.semilogx(freq, Af, color='k', marker='o', linestyle='None', label='measured')
ax.set_xlabel("f (Hz)")
ax.set_ylabel("|H|")
# ax.tick_params(axis='y')
ax.set_ylim([0, Hmax])
ax.grid(True, which='both', ls='--', alpha=0.4)
# combined legend
lines = ln_theo + ln_meas
labels = [l.get_label() for l in lines]
ax.legend(lines, labels, loc='best')
plt.title(f"2nd order {filter['label']} filter, Q={Q_meas:1.1f}")
plt.show()
