def funity_vs_scale2(op_in, op_load, op_tail, cload, phase_margin, fg=2):
s2min = 1
s2max = 40
num_s = 100
cmin = 1e-16
cmax = 1e-9
ctol = 1e-17
cstep = 1e-15
scale_load = op_in['ibias'] / op_load['ibias'] * fg
gfb = op_load['gm'] * scale_load
s2vec = np.linspace(s2min, s2max, num_s).tolist()
f0_list, pm0_list, f1_list, pm1_list, copt_list = [], [], [], [], []
for s2 in s2vec:
cir = LTICircuit()
cir.add_transistor(op_in, 'mid', 'in', 'gnd', 'gnd', fg=fg)
cir.add_transistor(op_load, 'mid', 'gnd', 'gnd', 'gnd', fg=scale_load)
cir.add_transistor(op_load,
'out',
'mid',
'gnd',
'gnd',
fg=scale_load * s2)
cir.add_transistor(op_tail, 'out', 'gnd', 'gnd', 'gnd', fg=fg * s2)
cir.add_cap(cload, 'out', 'gnd')
num, den = cir.get_num_den('in', 'out')
f0_list.append(get_w_crossings(num, den)[0] / (2 * np.pi))
pm0_list.append(get_stability_margins(num, den)[0])
cir.add_conductance(gfb * s2, 'mid', 'x')
copt = opt_cfb(phase_margin, cir, cmin, cmax, cstep, ctol)
if copt is None:
raise ValueError('oops, Cfb is None')
cir.add_cap(copt, 'x', 'out')
num, den = cir.get_num_den('in', 'out')
f1_list.append(get_w_crossings(num, den)[0] / (2 * np.pi))
pm1_list.append(get_stability_margins(num, den)[0])
copt_list.append(copt)
f, (ax0, ax1, ax2) = plt.subplots(3, sharex='all')
ax0.plot(s2vec, np.array(copt_list) * 1e15)
ax0.set_ylabel('Cf (fF)')
ax1.plot(s2vec, pm1_list, label='Cf')
ax1.plot(s2vec, pm0_list, label='no Cf')
ax1.legend()
ax1.set_ylabel('$\phi_{PM}$ (deg)')
ax2.plot(s2vec, np.array(f1_list) * 1e-9, label='Cf')
ax2.plot(s2vec, np.array(f0_list) * 1e-9, label='no Cf')
ax2.legend()
ax2.set_ylabel('$f_{UG}$ (GHz)')
ax2.set_xlabel('$I_2/I_1$')
plt.show()
def _get_ss_lti(self, op_dict:Mapping[str,Any],
nf_dict:Mapping[str,int],
cload:float) -> Tuple[float,float]:
ckt_p = self.make_ltickt(op_dict=op_dict, nf_dict=nf_dict, cload=cload, meas_side='p')
p_num, p_den = ckt_p.get_num_den(in_name='inp', out_name='out', in_type='v')
ckt_n = self.make_ltickt(op_dict=op_dict, nf_dict=nf_dict, cload=cload, meas_side='n')
n_num, n_den = ckt_n.get_num_den(in_name='inn', out_name='out', in_type='v')
num, den = num_den_add(p_num, np.convolve(n_num, [-1]),
p_den, n_den)
num = np.convolve(num, [0.5])
gain = num[-1]/den[-1]
wbw = get_w_3db(num, den)
pm, _ = get_stability_margins(num, den)
ugw, _ = get_w_crossings(num, den)
if wbw == None:
wbw = 0
fbw = wbw/(2*np.pi)
if ugw == None:
ugw = 0
ugf = ugw/(2*np.pi)
return gain, fbw, ugf, pm
def verify_closedLoop(n_op, p_op, tail_op,
nf_n, nf_p, nf_tail, pm_min,
cload, cn=165e-15, cp=83e-15, r=70.71e3):
'''
Inputs:
Outputs:
'''
ckt = construct_feedback(n_op, p_op, tail_op,
nf_n, nf_p, nf_tail,
cload)
loopBreak = ckt.get_transfer_function(in_name='inn', out_name='out',
in_type='v')
pm, gainm = get_stability_margins(loopBreak.num, loopBreak.den)
if pm < pm_min or isnan(pm):
return False, dict(pm=pm)
return True, dict(pm=pm)
def opt_cfb(phase_margin, cir, cmin, cmax, cstep, ctol):
bin_iter = FloatBinaryIterator(cmin, None, ctol, search_step=cstep)
while bin_iter.has_next():
cur_cf = bin_iter.get_next()
cir.add_cap(cur_cf, 'x', 'out')
num, den = cir.get_num_den('in', 'out')
cur_pm, _ = get_stability_margins(num, den)
if cur_pm < phase_margin:
if cur_cf > cmax:
# no way to make amplifier stable, just return
return None
bin_iter.up()
else:
bin_iter.save()
bin_iter.down()
cir.add_cap(-cur_cf, 'x', 'out')
return bin_iter.get_last_save()
def _get_ss_lti(self, op_dict:Mapping[str,Any],
nf_dict:Mapping[str,int],
opp_drain_conn:Mapping[str,str],
cload:float) -> Tuple[float,float,float]:
'''
Inputs:
op_dict: Dictionary of queried database operating points.
nf_dict: Dictionary of number of fingers for devices.
opp_drain_conn: Drain connection dictionary, a la n_drain_conn or p_drain_conn
cload: Load capacitance in farads.
Outputs:
gain: Calculated DC gain in V/V
fbw: Calculated 3dB frequency in Hz
ugf: Calculated unity gain frequency in Hz
pm: Simulated unity gain phase margin in degrees. Can also be NaN.
'''
ckt_p = self.make_ltickt(op_dict=op_dict, nf_dict=nf_dict, meas_side='p',
opp_drain_conn=opp_drain_conn, cload=cload)
p_num, p_den = ckt_p.get_num_den(in_name='inp', out_name='out', in_type='v')
ckt_n = self.make_ltickt(op_dict=op_dict, nf_dict=nf_dict, meas_side='n',
opp_drain_conn=opp_drain_conn, cload=cload)
n_num, n_den = ckt_n.get_num_den(in_name='inn', out_name='out', in_type='v')
# Superposition for inverting and noninverting inputs
num, den = num_den_add(p_num, np.convolve(n_num, [-1]),
p_den, n_den)
num = np.convolve(num, [0.5])
# Calculate figures of merit using the LTICircuit transfer function
gain = num[-1]/den[-1]
wbw = get_w_3db(num, den)
pm, _ = get_stability_margins(num, den)
if wbw == None:
wbw = 0
fbw = wbw/(2*np.pi)
ugw, _ = get_w_crossings(num, den)
if ugw == None:
ugw = 0
ugf = ugw/(2*np.pi)
return gain, fbw, ugf, pm
def _get_stb_lti(self, op_dict, nf_dict, ser_type, amp_in, cload, cdecap_amp, rsource) -> float:
'''
Returns:
pm: Phase margin (degrees)
'''
ckt = LTICircuit()
n_ser = ser_type == 'n'
n_amp = amp_in == 'n'
vdd = 'vdd' if rsource != 0 else 'gnd'
# Series device
ser_d = vdd if n_ser else 'reg'
ser_s = 'reg' if n_ser else vdd
ckt.add_transistor(op_dict['ser'], ser_d, 'out', ser_s, fg=nf_dict['ser'], neg_cap=False)
# Passives
ckt.add_cap(cload, 'reg', 'gnd')
ckt.add_cap(cdecap_amp, 'out', 'reg')
if rsource != 0:
ckt.add_res(rsource, 'gnd', 'vdd')
# Amplifier
tail_rail = 'gnd' if n_amp else vdd
load_rail = vdd if n_amp else 'gnd'
inp_conn = 'gnd' if n_ser else 'amp_in'
inn_conn = 'gnd' if not n_ser else 'amp_in'
ckt.add_transistor(op_dict['amp_in'], 'outx', inp_conn, 'tail', fg=nf_dict['amp_in'], neg_cap=False)
ckt.add_transistor(op_dict['amp_in'], 'out', inn_conn, 'tail', fg=nf_dict['amp_in'], neg_cap=False)
ckt.add_transistor(op_dict['amp_tail'], 'tail', 'gnd', tail_rail, fg=nf_dict['amp_tail'], neg_cap=False)
ckt.add_transistor(op_dict['amp_load'], 'outx', 'outx', load_rail, fg=nf_dict['amp_load'], neg_cap=False)
ckt.add_transistor(op_dict['amp_load'], 'out', 'outx', load_rail, fg=nf_dict['amp_load'], neg_cap=False)
# Calculating stability margins
num, den = ckt.get_num_den(in_name='amp_in', out_name='reg', in_type='v')
pm, _ = get_stability_margins(np.convolve(num, [-1]), den)
return pm
def design_inverter_tia_lti(db_n, db_p, sim_env,
vg_res, rf_res,
vdd, cpd, cload,
rdc_min, fbw_min, pm_min,
vb_n, vb_p):
"""
Designs a transimpedance amplifier with an inverter amplifier
in resistive feedback. Uses the LTICircuit functionality.
Inputs:
db_n/p: Databases for NMOS and PMOS device characterization data,
respectively.
sim_env: Simulation corner.
vg_res: Float. Step resolution when sweeping gate voltage.
rf_res: Float. Step resolution when sweeping feedback resistance.
vdd: Float. Supply voltage.
cpd: Float. Input parasitic capacitance.
cload: Float. Output load capacitance.
rdc_min: Float. Minimum DC transimpedance.
fbw_min: Float. Minimum bandwidth (Hz).
pm_min: Float. Minimum phase margin.
vb_n/p: Float. Back-gate/body voltage of NMOS and PMOS, respectively.
Raises:
ValueError: If unable to meet the specification requirements.
Returns:
A dictionary with the following key:value pairings:
vg: Float. Input bias voltage.
nf_n: Integer. NMOS number of channel fingers.
nf_p: Integer. PMOS number of channel fingers.
rf: Float. Value of feedback resistor.
rdc: Float. Expected DC transimpedance.
fbw: Float. Expected bandwidth (Hz).
pm: Float. Expected phase margin.
ibias: Float. Expected DC bias current.
"""
ibn_fun = db_n.get_function('ibias', env=sim_env)
ibp_fun = db_p.get_function('ibias', env=sim_env)
# Get sweep values (Vg, Vd)
vg_min = 0
vg_max = vdd
vg_vec = np.arange(vg_min, vg_max, vg_res)
nf_n_vec = np.arange(1, 20, 1) # DEBUGGING: Is there a non-brute force way of setting this?
# Find the best operating point
best_ibias = float('inf')
best_op = None
for vg in vg_vec:
vdd_vd_ratio = vdd/vg
#print("\nVD/VG: {}".format(vg))
n_op_info = db_n.query(vgs=vg, vds=vg, vbs=vb_n-0)
p_op_info = db_p.query(vgs=vg-vdd, vds=vg-vdd, vbs=vb_p-vdd)
# Find ratio of fingers to get desired output common mode
ibias_n = n_op_info['ibias']
ibias_p = p_op_info['ibias']
pn_match = abs(ibias_n/ibias_p)
pn_ratio = pn_match/(vdd_vd_ratio - 1) # DEBUGGING: Won't be exact
if pn_ratio == 0:
continue
# Sweep the number of fingers to minimize power
for nf_n in nf_n_vec:
nf_p = int(round(nf_n * pn_ratio))
if nf_p <= 0:
continue
ibias_error = abs(abs(ibias_p)*nf_p-abs(ibias_n)*nf_n)/(abs(ibias_n)*nf_n)
if ibias_error > 0.05:
continue
print("N/P: {}/{} fingers".format(nf_n, nf_p))
# Finding amplifier ss parameters
inv = LTICircuit()
inv.add_transistor(n_op_info, 'out', 'in', 'gnd', fg=nf_n)
inv.add_transistor(p_op_info, 'out', 'in', 'gnd', fg=nf_p)
inv_num, inv_den = inv.get_num_den(in_name='in', out_name='out', in_type='v')
A0 = abs(inv_num[-1]/inv_den[-1])
gds_n = n_op_info['gds'] * nf_n
gm_n = n_op_info['gm'] * nf_n
cgs_n = n_op_info['cgs'] * nf_n
cgd_n = n_op_info['cgd'] * nf_n
cds_n = n_op_info['cds'] * nf_n
cgb_n = n_op_info.get('cgb', 0) * nf_n
cdb_n = n_op_info.get('cdb', 0) * nf_n
cdd_n = n_op_info['cdd'] * nf_n
cgg_n = n_op_info['cgg'] * nf_n
gds_p = p_op_info['gds'] * nf_p
gm_p = p_op_info['gm'] * nf_p
cgs_p = p_op_info['cgs'] * nf_p
cgd_p = p_op_info['cgd'] * nf_p
cds_p = p_op_info['cds'] * nf_p
cgb_p = p_op_info.get('cgb', 0) * nf_p
cdb_p = p_op_info.get('cdb', 0) * nf_p
cdd_p = p_op_info['cdd'] * nf_p
cgg_p = p_op_info['cgg'] * nf_p
gm = abs(gm_n) + abs(gm_p)
gds = abs(gds_n) + abs(gds_p)
ro = 1/gds
cgs = cgs_n + cgs_p
cds = cds_n + cds_p
cgb = cgb_n + cgb_p
cdb = cdb_n + cdb_p
cgd = cgd_n + cgd_p
cdd = cdd_n + cdd_p
cgg = cgg_n + cgg_p
# Assume Rdc is negative, bound Rf
rf_min = max(rdc_min*(1+A0)/A0 + ro/A0, 0)
rf_vec = np.arange(rf_min, rdc_min*5, rf_res)
# Sweep values of Rf to check f3dB and PM spec
for rf in rf_vec:
# Circuit for GBW
circuit = LTICircuit()
circuit.add_transistor(n_op_info, 'out', 'in', 'gnd', fg=nf_n)
circuit.add_transistor(p_op_info, 'out', 'in', 'gnd', fg=nf_p)
circuit.add_res(rf, 'in', 'out')
circuit.add_cap(cpd, 'in', 'gnd')
circuit.add_cap(cload, 'out', 'gnd')
# Determining if it meets spec
num, den = circuit.get_num_den(in_name='in', out_name='out', in_type='i')
rdc = num[-1]/den[-1]
if abs(rdc) < rdc_min-1e-8:
print("RDC: {0:.2f} (FAIL)\n".format(rdc))
continue
else:
print("RDC: {0:.2f}".format(rdc))
fbw = get_w_3db(num, den)/(2*np.pi)
if fbw < fbw_min or isnan(fbw):
print("BW: {} (FAIL)\n".format(fbw))
break # Increasing Rf isn't going to help
else:
print("BW: {}".format(fbw))
# Circuit for phase margin
# miller = (1-gm*rf)/(ro+rf)*ro
circuit2 = LTICircuit()
circuit2.add_conductance(gds, 'out', 'gnd')
circuit2.add_cap(cgg+cpd, 'in', 'gnd')
circuit2.add_cap(cdd+cload, 'out', 'gnd')
circuit2.add_cap(cgd, 'in', 'out')
circuit2.add_res(rf, 'in', 'out')
loopBreak = circuit2.get_transfer_function(in_name='out', out_name='in', in_type='i')
pm, gainm = get_stability_margins(loopBreak.num*gm, loopBreak.den)
if pm < pm_min or isnan(pm):
print("PM: {} (FAIL)\n".format(pm))
continue
else:
print("PM: {}\n".format(pm))
if ibias_n*nf_n < best_ibias:
best_ibias = ibias_n*nf_n
best_op = dict(
vg=vg,
nf_n=nf_n,
nf_p=nf_p,
rf=rf,
rdc=rdc,
fbw=fbw,
pm=pm,
ibias=best_ibias)
if best_op == None:
raise ValueError("No solutions.")
return best_op
def _find_rz_cf(self,
gm_db,
load_db,
vtail_list,
vg_list,
vmid_list,
vout_list,
vbias_list,
vb_gm,
vb_load,
cload,
cpar1,
w_dict,
th_dict,
stack_dict,
seg_dict,
gm2_list,
res_var,
phase_margin,
cap_tol=1e-15,
cap_step=10e-15,
cap_min=1e-15,
cap_max=1e-9):
"""Find minimum miller cap that stabilizes the system.
NOTE: This function assume phase of system for any miller cap value will not loop
around 360, otherwise it may get the phase margin wrong. This assumption should be valid
for this op amp.
"""
gz_worst = float(min(gm2_list))
gz_nom = gz_worst * (1 - res_var)
# find maximum Cf needed to stabilize all corners
cf_min = cap_min
for env_idx, (vtail, vg, vmid, vout, vbias) in \
enumerate(zip(vtail_list, vg_list, vmid_list, vout_list, vbias_list)):
cir = self._make_circuit(env_idx, gm_db, load_db, vtail, vg, vmid,
vout, vbias, vb_gm, vb_load, cload, cpar1,
w_dict, th_dict, stack_dict, seg_dict,
gz_worst)
bin_iter = FloatBinaryIterator(cf_min,
None,
cap_tol,
search_step=cap_step)
while bin_iter.has_next():
cur_cf = bin_iter.get_next()
cir.add_cap(cur_cf, 'outp', 'xp')
cir.add_cap(cur_cf, 'outn', 'xn')
num, den = cir.get_num_den('in', 'out')
cur_pm, _ = get_stability_margins(num, den)
if cur_pm < phase_margin:
if cur_cf > cap_max:
# no way to make amplifier stable, just return
return None, None, None, None, None, None
bin_iter.up()
else:
bin_iter.save()
bin_iter.down()
cir.add_cap(-cur_cf, 'outp', 'xp')
cir.add_cap(-cur_cf, 'outn', 'xn')
# bin_iter is guaranteed to save at least one value, so don't need to worry about
# cf_min being None
cf_min = bin_iter.get_last_save()
# find gain, unity gain bandwidth, and phase margin across corners
gain_list, f3db_list, funity_list, pm_list = [], [], [], []
for env_idx, (vtail, vg, vmid, vout, vbias) in \
enumerate(zip(vtail_list, vg_list, vmid_list, vout_list, vbias_list)):
cir = self._make_circuit(env_idx, gm_db, load_db, vtail, vg, vmid,
vout, vbias, vb_gm, vb_load, cload, cpar1,
w_dict, th_dict, stack_dict, seg_dict,
gz_nom)
cir.add_cap(cf_min, 'outp', 'xp')
cir.add_cap(cf_min, 'outn', 'xn')
num, den = cir.get_num_den('in', 'out')
pn = np.poly1d(num)
pd = np.poly1d(den)
gain_list.append(abs(pn(0) / pd(0)))
f3db_list.append(get_w_3db(num, den) / 2 / np.pi)
funity_list.append(get_w_crossings(num, den)[0] / 2 / np.pi)
pm_list.append(get_stability_margins(num, den)[0])
return funity_list, 1 / gz_nom, cf_min, gain_list, f3db_list, pm_list
def design_inv_tia(specs, pch_op_info, nch_op_info, pch_scale):
sim_env = specs['sim_env']
pch_db = specs['pch_db']
nch_db = specs['nch_db']
vgs_res = specs['vgs_res']
vdd = specs['vdd']
rdc_targ = specs['rdc']
f3db_targ = specs['f3db']
pm_targ = specs['pm']
cin = specs['cin']
cl = specs['cl']
scale_min = specs['scale_min']
scale_max = specs['scale_max']
n_scale = specs['n_scale']
rf_min = specs['rf_min']
rf_max = specs['rf_max']
n_rf = specs['n_rf']
pch_ibias = pch_op_info['ibias']
nch_ibias = nch_op_info['ibias']
gmp = pch_op_info['gm'] * pch_scale
gmn = nch_op_info['gm']
gm_tot = gmp + gmn
gdsp = pch_op_info['gds'] * pch_scale
gdsn = nch_op_info['gds']
rop = 1 / gdsp
ron = 1 / gdsn
ro_tot = rop * ron / (rop + ron)
gds_tot = 1 / ro_tot
cgsp = pch_op_info['cgs'] * pch_scale
cgsn = nch_op_info['cgs']
cgs_tot = cgsp + cgsn
cgbp = pch_op_info['cgb'] * pch_scale
cgbn = nch_op_info['cgb']
cgb_tot = cgbp + cgbn
cgdp = pch_op_info['cgd'] * pch_scale
cgdn = nch_op_info['cgd']
cgd_tot = cgdp + cgdn
cggp = pch_op_info['cgg'] * pch_scale
cggn = nch_op_info['cgg']
cgg_tot = cggp + cggn
cdsp = pch_op_info['cds'] * pch_scale
cdsn = nch_op_info['cds']
cds_tot = cdsp + cdsn
cdbp = pch_op_info['cdb'] * pch_scale
cdbn = nch_op_info['cdb']
cdb_tot = cdbp + cdbn
cddp = pch_op_info['cdd'] * pch_scale
cddn = nch_op_info['cdd']
cdd_tot = cddp + cddn
scale_vec = np.linspace(scale_min, scale_max, n_scale)
for scale in scale_vec:
for rf in np.linspace(rf_min, rf_max, n_rf):
# Build circuit
cir = LTICircuit()
cir.add_transistor(pch_op_info,
'out',
'in',
'gnd',
'gnd',
fg=scale * pch_scale)
cir.add_transistor(nch_op_info,
'out',
'in',
'gnd',
'gnd',
fg=scale)
cir.add_res(rf, 'out', 'in')
cir.add_cap(cin, 'in', 'gnd')
cir.add_cap(cl, 'out', 'gnd')
# Get gain/poles/zeros/Bode plot
# Note: any in_type other than 'v' results in current source input
tf = cir.get_transfer_function('in', 'out', in_type='i')
rdc = np.absolute(tf.num[-1] / tf.den[-1])
w3db = get_w_3db(tf.num, tf.den)
f3db = w3db / (2 * np.pi)
cin_tot = cin + cgg_tot * scale
cl_tot = cl + cdd_tot * scale
cgd_scaled = cgd_tot * scale
gm_scaled = gm_tot * scale
gds_scaled = gds_tot * scale
cir_open_loop = LTICircuit()
cir_open_loop.add_vccs(gm_scaled, 'out', 'gnd', 'vt', 'gnd')
cir_open_loop.add_conductance(gds_scaled, 'out', 'gnd')
cir_open_loop.add_cap(cl_tot, 'out', 'gnd')
cir_open_loop.add_res(rf, 'out', 'vr')
cir_open_loop.add_cap(cgd_scaled, 'out', 'vr')
cir_open_loop.add_cap(cin_tot, 'vr', 'gnd')
tf_open_loop = cir_open_loop.get_transfer_function('vt',
'vr',
in_type='v')
pm, gain_margin = get_stability_margins(tf_open_loop.num,
tf_open_loop.den)
pm = pm - 180
if rdc >= rdc_targ and f3db >= f3db_targ and pm >= pm_targ:
ibias = scale * nch_ibias
design = dict(IB=ibias,
Scale=scale,
Rf=rf,
RDC=rdc,
f3dB=f3db,
PM=pm)
return design
def _get_stb_lti(self, op_dict, nf_dict, series_type, rload,
cload) -> float:
'''
Returns:
pm: Phase margins (in degrees)
'''
ckt = LTICircuit()
n_ser = series_type == 'n'
# Series device
ser_d = 'gnd' if n_ser else 'reg'
ser_s = 'reg' if n_ser else 'gnd'
ckt.add_transistor(op_dict['ser'],
ser_d,
'out',
ser_s,
fg=nf_dict['ser'],
neg_cap=False)
# Load passives
ckt.add_res(rload, 'reg', 'gnd')
ckt.add_cap(rload, 'reg', 'gnd')
# TODO include any compensation passives
# Amplifier
inp_conn = 'gnd' if n_ser else 'in'
inn_conn = 'gnd' if not n_ser else 'in'
ckt.add_transistor(op_dict['in'],
'outx',
inp_conn,
'tail',
fg=nf_dict['in'],
neg_cap=False)
ckt.add_transistor(op_dict['in'],
'out',
inn_conn,
'tail',
fg=nf_dict['in'],
neg_cap=False)
ckt.add_transistor(op_dict['tail'],
'tail',
'gnd',
'gnd',
fg=nf_dict['tail'],
neg_cap=False)
ckt.add_transistor(op_dict['load'],
'outx',
'outx',
'gnd',
fg=nf_dict['load'],
neg_cap=False)
ckt.add_transistor(op_dict['load'],
'out',
'outx',
'gnd',
fg=nf_dict['load'],
neg_cap=False)
# Calculating stability margins
num, den = ckt.get_num_den(in_name='in', out_name='reg', in_type='v')
pm, _ = get_stability_margins(np.convolve(num, [-1]), den)
return pm
def design_inv_tia(specs, pch_op_info, nch_op_info, pch_scale):
sim_env = specs['sim_env']
pch_db = specs['pch_db']
nch_db = specs['nch_db']
vgs_res = specs['vgs_res']
vdd = specs['vdd']
isw = specs['isw']
ber_targ = specs['ber']
voff = specs['voff']
snr_like_targ = specs['snr_like']
pmos_noise_scale = specs['pmos_noise_scale']
# rdc_targ = specs['rdc']
noise_const = specs['noise_const']
tper = specs['tper']
f_factor = specs['f_factor']
# f3db_targ = specs['f3db']
f3db_targ = f_factor * 1 / tper
pm_targ = specs['pm']
cin = specs['cin']
cl = specs['cl']
scale_min = specs['scale_min']
scale_max = specs['scale_max']
n_scale = specs['n_scale']
rf_min = specs['rf_min']
rf_max = specs['rf_max']
n_rf = specs['n_rf']
pch_ibias = pch_op_info['ibias']
nch_ibias = nch_op_info['ibias']
gmp = pch_op_info['gm'] * pch_scale
gmn = nch_op_info['gm']
gm_tot = gmp + gmn
gammap = pch_op_info['gamma']
gamman = nch_op_info['gamma']
gdsp = pch_op_info['gds'] * pch_scale
gdsn = nch_op_info['gds']
rop = 1 / gdsp
ron = 1 / gdsn
ro_tot = rop * ron / (rop + ron)
gds_tot = 1 / ro_tot
cgsp = pch_op_info['cgs'] * pch_scale
cgsn = nch_op_info['cgs']
cgs_tot = cgsp + cgsn
cgbp = pch_op_info['cgb'] * pch_scale
cgbn = nch_op_info['cgb']
cgb_tot = cgbp + cgbn
cgdp = pch_op_info['cgd'] * pch_scale
cgdn = nch_op_info['cgd']
cgd_tot = cgdp + cgdn
cggp = pch_op_info['cgg'] * pch_scale
cggn = nch_op_info['cgg']
cgg_tot = cggp + cggn
cdsp = pch_op_info['cds'] * pch_scale
cdsn = nch_op_info['cds']
cds_tot = cdsp + cdsn
cdbp = pch_op_info['cdb'] * pch_scale
cdbn = nch_op_info['cdb']
cdb_tot = cdbp + cdbn
cddp = pch_op_info['cdd'] * pch_scale
cddn = nch_op_info['cdd']
cdd_tot = cddp + cddn
scale_vec = np.linspace(scale_min, scale_max, n_scale)
for scale in scale_vec:
for rf in np.linspace(rf_max, rf_min, n_rf):
# Build circuit
cir = LTICircuit()
cir.add_transistor(pch_op_info,
'out',
'in',
'gnd',
'gnd',
fg=scale * pch_scale)
cir.add_transistor(nch_op_info,
'out',
'in',
'gnd',
'gnd',
fg=scale)
cir.add_res(rf, 'out', 'in')
cir.add_cap(cin, 'in', 'gnd')
cir.add_cap(cl, 'out', 'gnd')
# Get gain/poles/zeros/Bode plot
# Note: any in_type other than 'v' results in current source input
tf = cir.get_transfer_function('in', 'out', in_type='i')
rdc = np.absolute(tf.num[-1] / tf.den[-1])
w3db = get_w_3db(tf.num, tf.den)
f3db = w3db / (2 * np.pi)
if f3db >= f3db_targ:
# Noise
in_gmp = noise_const * gammap * gmp
in_gmn = noise_const * gamman * gmn
in_rf = noise_const / rf
tf_gm = cir.get_transfer_function('out', 'out', in_type='i')
dc_gm = tf_gm.num[-1] / tf_gm.den[-1]
wo2_gm = tf_gm.den[-1] / tf_gm.den[0]
woQ_gm = tf_gm.den[-1] / tf_gm.den[1]
wz_gm = tf_gm.num[-1] / tf_gm.num[0]
von_gmp = pmos_noise_scale * in_gmp * dc_gm**2 * woQ_gm / 4 * (
wo2_gm / wz_gm**2 + 1)
von_gmn = in_gmn * dc_gm**2 * woQ_gm / 4 * (wo2_gm / wz_gm**2 +
1)
cir.add_vccs(1, 'out', 'in', 'vn', 'gnd')
tf_rf = cir.get_transfer_function('vn', 'out', in_type='v')
dc_rf = tf_rf.num[-1] / tf_rf.den[-1]
wo2_rf = tf_rf.den[-1] / tf_rf.den[0]
woQ_rf = tf_rf.den[-1] / tf_rf.den[1]
wz_rf = tf_rf.num[-1] / tf_rf.num[0]
von_rf = in_rf * dc_rf**2 * woQ_rf / 4 * (wo2_rf / wz_rf**2 +
1)
von = von_gmp + von_gmn + von_rf
# Signal
vo = isw * rdc
snr_like = (vo - voff) / np.sqrt(von)
if snr_like >= snr_like_targ:
cin_tot = cin + cgg_tot * scale
cl_tot = cl + cdd_tot * scale
cgd_scaled = cgd_tot * scale
gm_scaled = gm_tot * scale
gds_scaled = gds_tot * scale
# Build open loop circuit for phase margin
cir_open_loop = LTICircuit()
cir_open_loop.add_vccs(gm_scaled, 'out', 'gnd', 'vt',
'gnd') # ***
cir_open_loop.add_conductance(gds_scaled, 'out', 'gnd')
cir_open_loop.add_cap(cl_tot, 'out', 'gnd')
cir_open_loop.add_res(rf, 'out', 'vr')
cir_open_loop.add_cap(cgd_scaled, 'out', 'vr')
cir_open_loop.add_cap(cin_tot, 'vr', 'gnd')
tf_open_loop = cir_open_loop.get_transfer_function(
'vt', 'vr', in_type='v')
pm, gm = get_stability_margins(tf_open_loop.num,
tf_open_loop.den)
pm = pm - 180
if pm >= pm_targ:
ibias = scale * nch_ibias
design = dict(IB=ibias,
Scale=scale,
Rf=rf,
RDC=rdc,
f3dB=f3db,
PM=pm,
Von_Rf=von_rf,
Von_gmp=von_gmp,
Von_gmn=von_gmn,
Von=von,
SNR_Like=snr_like)
return design
def design_LPF_AMP(db_n, db_p, db_bias, sim_env,
vin, vdd_nom, vdd_vec, cload,
gain_min, fbw_min, pm_min,
vb_n, vb_p, error_tol=0.1, ibias_max=20e-6):
'''
Designs an amplifier with an N-input differential pair
with a source follower. Uses the LTICircuit functionality.
Inputs:
db_n/p: Databases for non-biasing NMOS and PMOS device
characterization data, respectively.
db_bias: Database for tail NMOS device characterization data.
sim_env: Simulation corner.
vin: Float. Input (and output and tail) bias voltage in volts.
vtail_res: Float. Step resolution in volts when sweeping tail voltage.
vdd_nom: Float. Nominal supply voltage in volts.
vdd_vec: Collection of floats. Elements should include the min and
max supply voltage in volts.
cload: Float. Output load capacitance in farads.
gain_min: Float. Minimum DC voltage gain in V/V.
fbw_min: Float. Minimum bandwidth (Hz).
pm_min: Float. Minimum phase margin in degrees.
vb_n/p: Float. Back-gate/body voltage (V) of NMOS and PMOS,
respectively (nominal).
error_tol: Float. Fractional tolerance for ibias error when computing
the p-to-n ratio.
ibias_max: Float. Maximum bias current (A) allowed with nominal vdd.
Raises:
ValueError: If unable to meet the specification requirements.
Outputs:
A dictionary with the following key:value pairings:
nf_cs_n/pB/nB: Integer. Number of minimum device widths for common source
N-input/active P-load/tail device.
nf_sfN_n/pB/nB: Integer. Number of minimum device widths for source follower
N-input/P-bias/N-bias.
nf_sfP_p/pB/nB: Integer. Number of minimum device widths for source follower
P-input/P-bias/N-bias.
vtail: Float. DC tail voltage for the common source stage.
This value is reused throughout the circuit.
gain_cs: Float. DC voltage gain of the CS amplifier (V/V).
gain_sfN: Float. DC voltage gain of the first source follower (V/V).
gain_sfP: Float. DC voltage gain of the second source follower (V/V).
gain: Float. DC voltage gain of both stages combined (V/V).
fbw: Float. Bandwdith (Hz).
pm: Float. Phase margin (degrees) for unity gain.
'''
possibilities = []
ibias_budget = ibias_max
# Given this amplifier will be unity gain feedback at DC
vout = vin
vstar_min = 0.15
vtail_vec = np.arange(vstar_min, vout, vtail_res)
for vtail in vtail_vec:
print("\nVTAIL: {0}".format(vtail))
n_op = db_n.query(vgs=vin-vtail, vds=vout-vtail, vbs=vb_n-vtail)
p_B_op = db_p.query(vgs=vout-vdd_nom, vds=vout-vdd_nom, vbs=vb_p-vdd_nom)
n_B_op = db_bias.query(vgs=vout-0, vds=vtail-0, vbs=vb_n-0)
p_op = db_p.query(vgs=vtail-vout, vds=vtail-vout, vbs=vb_p-vout)
# Finding the ratio between devices to converge to correct biasing
idn_base = n_op['ibias']
idp_B_base = p_B_op['ibias']
idn_B_base = n_B_op['ibias']
idp_base = p_op['ibias']
pB_to_n = abs(idn_base/idp_B_base)
nB_to_n = abs(idn_base/idn_B_base)
pB_to_p = abs(idp_base/idp_B_base)
nB_to_p = abs(idp_base/idn_B_base)
### P-input SF ###
sfP_mult_max = int(round(abs(ibias_budget/idn_base)))
sfP_mult_vec = np.arange(1, sfP_mult_max, 1)
for sfP_mult in sfP_mult_vec in
nf_sfP_p = sfP_mult
# Verify that the sizing is feasible and gets sufficiently
# good current matching
pB_sfP_good, nf_sfP_pB = verify_ratio(idp_base, idp_B_base, pB_to_p,
nf_sfP_p, error_tol)
nB_sfP_good, nf_sfP_nB = verify_ratio(idp_base, idn_B_base, nB_to_p,
nf_sfP_p, error_tol)
if not (pB_sfP_good and nB_sfP_good):
continue
# Check SF2 bandwidth; size up until it meets
ckt = construct_sfP_LTI(p_op, p_B_op, n_B_op,
nf_sfP_p, nf_sfP_pB, nf_sfP_nB,
cload)
sfP_num, sfP_den = ckt.get_num_den(in_name='out2', out_name='out', in_type='v')
fbw_sfP = get_w_3db(sfP_num, sfP_den)/(2*np.pi)
# No need to keep sizing up
if fbw_sfP >= fbw_min:
break
# Final stage can never meet bandwidth given biasing
if fbw_sfP < fbw_min:
print("SFP: BW failure\n")
continue
# Sizing ratio failure
if 0 in [nf_sfP_pB, nf_sfP_nB]:
print("SFP: sizing ratio failure\n")
continue
ibias_sfP = idp_base * nf_sfP_p
ibias_budget = ibias_budget - ibias_sfP
print("Remaining budget\t:\t {0}".format(ibias_budget))
### N-input SF ###
sfN_mult_max = int(round(abs(ibias_budget/idn_base)))
sfN_mult_vec = np.arange(1, sfN_mult_max, 1)
for sfN_mult in sfN_mult_vec:
nf_sfN_n = sfN_mult
# Repeat the same feasibility + current matching check
pB_sfN_good, nf_sfN_pB = verify_ratio(idn_base, idp_B_base,
pB_to_n, nf_sfN_n, error_tol)
nB_sfN_good, nf_sfN_pN = verify_ratio(idn_base, idn_B_base,
nB_to_n, nf_sfN_n, error_tol)
if not (pB_sfn_good and nB_sfN_good):
continue
# Check SF1 bandwidth; size up until it meets
ckt = construct_sfN_LTI(p_op, p_B_op, n_B_op,
nf_sfP_p, nf_sfP_pB, nf_sfP_nB,
cload,
n_op,
nf_sfN_n, nf_sfN_pB, nf_sfN_nB)
sfN_num, sfN_den = ckt.get_num_den(in_name='out1', out_name='out', in_type='v')
fbw_sfN = get_w_3db(sfN_num, sfN_den)/(2*np.pi)
# No need to keep sizing up
if fbw_sfN >= fbw_min:
break
# Second stage can never meet bandwidth given restrictions
if fbw_sfN < fbw_min:
print("SFN: BW failure\n")
continue
# Sizing ratio failure
if 0 in [nf_sfN_pB, nf_sfN_nB]:
print("SFN: sizing ratio failure\n")
continue
ibias_sfN = idn_base * nf_sfN_n
ibias_budget = ibias_budget - ibias_sfN
print("Remaining budget\t:\t {0}".format(ibias_budget))
### CS input ###
cs_mult_max = int(round(abs(ibias_budget/idn_base)))
cs_mult_vec = np.arange(1, cs_mult_max, 1)
for cs_mult in cs_mult_vec:
nf_cs_n = cs_mult_vec
# Verify that the sizing is feasible and gets sufficiently
# good current matching
pB_cs_good, nf_cs_pB = verify_ratio(idn_base, idp_B_base, pB_to_n, nf_cs_n,
error_tol)
nB_cs_good, nf_cs_nB = verify_ratio(idn_base, idn_B_base, nB_to_n, nf_cs_n*2,
error_tol)
if not (pB_cs_good and nB_cs_good):
continue
# Check combined stages' small signal
ckt = construct_total_LTI(p_op, p_B_op, n_B_op,
nf_sfP_p, nf_sfP_pB, nf_sfP_nB,
cload,
n_op,
nf_sfN_n, nf_sfN_pB, nf_sfN_nB,
nf_cs_n, nf_cs_pB, nf_cs_nB)
total_num, total_den = ckt.get_num_den(in_name='in', out_name='out', in_type='v')
# Check cumulative gain
gain_total = abs(total_num[-1]/total_den[-1])
if gain_total < gain_min:
print("CS: A0 failure {0}\n".format(gain_total))
break # Biasing sets the gain
# Check cumulative bandwidth
fbw_total = get_w_3db(total_num, total_den)/(2*np.pi)
if fbw_total < fbw_min:
print("CS: BW failure {0}\n".format(fbw_total))
continue
# Check phase margin (TODO?)
loopBreak = ckt.get_transfer_function(in_name='out', out_name='in', in_type='v')
pm, gainm = get_stability_margins(loopBreak.num, loopBreak.den)
if pm < pm_min or isnan(pm):
print("CS: PM failure {0}\n".format(pm))
continue
# If gain, bw, and PM are met, no need to keep sizing up
break
# Sizing ratio failure
if 0 in [nf_cs_pB, nf_cs_nB]:
print("CS: sizing ratio failure\n")
continue
# Iterated, biasing condition + constraints can't meet spec
if fbw_total < fbw_min or gain_total < gain_min or pm < pm_min:
continue
else:
print("HALLELUJAH SUCCESS\n")
cs_num, cs_den = ckt.get_num_den(in_name='in', out_name='out1', in_type='v')
sfN_num, sfN_den = ckt.get_num_den(in_name='out1', out_name='out2', in_type='v')
sfP_num, sfP_den = ckt.get_num_den(in_name='out2', out_name='out', in_type='v')
gain_cs = abs(cs_num[-1]/cs_den[-1])
gain_sfN = abs(sfN_num[-1]/sfN_den[-1])
gain_sfP = abs(sfP_num[-1]/sfP_den[-1])
viable = dict(
nf_cs_n = nf_cs_n,
nf_cs_pB = nf_cs_pB,
nf_cs_nB = nf_cs_nB,
nf_sfN_n = nf_sfN_n,
nf_sfN_pB = nf_sfN_pB,
nf_sfN_nB = nf_sfN_nB,
nf_sfP_p = nf_sfP_p,
nf_sfP_pB = nf_sfP_pB,
nf_sfP_nB = nf_sfP_nB,
vtail = vtail,
gain_cs = gain_cs,
gain_sfN = gain_sfN,
gain_sfP = gain_sfP,
gain = gain_total,
fbw = fbw_total,
pm = pm)
pprint.pprint(viable)
print("\n")
possibilities.append([viable])
# TODO: Check all other VDDs
return possibilities
def verify_TIA_inverter_SS(n_op_info, p_op_info, nf_n, nf_p, rf, cpd, cload,
rdc_min, fbw_min, pm_min):
"""
Inputs:
n/p_op_info: The MOSDBDiscrete library for the NMOS and PMOS
devices in the bias point for verification.
nf_n/p: Integer. Number of channel fingers for the NMOS/PMOS.
rf: Float. Value of the feedback resistor in ohms.
cpd: Float. Input capacitance not from the TIA in farads.
cload: Float. Output capacitance not from the TIA in farads.
rdc_min: Float. Minimum DC transimpedance in ohms.
fbw_min: Float. Minimum bandwidth (Hz).
pm_min: Float. Minimum phase margin in degrees.
Outputs:
Returns two values
The first is True if the spec is met, False otherwise.
The second is a dictionary of values for rdc (DC transimpedance, V/I),
bw (bandwidth, Hz), and pm (phase margin, deg) if computed. None otherwise.
"""
# Getting relevant small-signal parameters
gds_n = n_op_info['gds'] * nf_n
gds_p = p_op_info['gds'] * nf_p
gds = gds_n + gds_p
gm_n = n_op_info['gm'] * nf_n
gm_p = p_op_info['gm'] * nf_p
gm = gm_n + gm_p
cgs_n = n_op_info['cgs'] * nf_n
cgs_p = p_op_info['cgs'] * nf_p
cgs = cgs_n + cgs_p
cds_n = n_op_info['cds'] * nf_n
cds_p = p_op_info['cds'] * nf_p
cds = cds_n + cds_p
cgd_n = n_op_info['cgd'] * nf_n
cgd_p = p_op_info['cgd'] * nf_p
cgd = cgd_n + cgd_p
# Circuit for GBW
circuit = LTICircuit()
circuit.add_transistor(n_op_info, 'out', 'in', 'gnd', fg=nf_n)
circuit.add_transistor(p_op_info, 'out', 'in', 'gnd', fg=nf_p)
circuit.add_res(rf, 'in', 'out')
circuit.add_cap(cpd, 'in', 'gnd')
circuit.add_cap(cload, 'out', 'gnd')
# Check gain
num, den = circuit.get_num_den(in_name='in', out_name='out', in_type='i')
rdc = num[-1] / den[-1]
if abs(round(rdc)) < round(rdc_min):
print("GAIN:\t{0} (FAIL)".format(rdc))
return False, dict(rdc=rdc, fbw=None, pm=None)
# Check bandwidth
fbw = get_w_3db(num, den) / (2 * np.pi)
if fbw < fbw_min or np.isnan(fbw):
print("BW:\t{0} (FAIL)".format(fbw))
return False, dict(rdc=rdc, fbw=fbw, pm=None)
# Check phase margin by constructing an LTICircuit first
circuit2 = LTICircuit()
"""circuit2.add_transistor(n_op_info, 'out', 'in', 'gnd', fg=nf_n)
circuit2.add_transistor(p_op_info, 'out', 'in', 'gnd', fg=nf_p)
circuit2.add_cap(cpd, 'in', 'gnd')
circuit2.add_cap(cload, 'out', 'gnd')
circuit2.add_res(rf, 'in', 'break')
# Cancel Cgd to correctly break loop
circuit2.add_cap(-cgd, 'in' , 'out')
circuit.add_cap(cgd, 'in', 'break')"""
circuit2.add_conductance(gds, 'out', 'gnd')
circuit2.add_cap(cgs + cpd, 'in', 'gnd')
circuit2.add_cap(cds + cload, 'out', 'gnd')
circuit2.add_cap(cgd, 'in', 'out')
circuit2.add_res(rf, 'in', 'out')
loopBreak = circuit2.get_transfer_function(in_name='in',
out_name='out',
in_type='i')
pm, gainm = get_stability_margins(loopBreak.num * gm, loopBreak.den)
if pm < pm_min or np.isnan(pm):
print("PM:\t{0} (FAIL)\n".format(pm))
return False, dict(rdc=rdc, fbw=fbw, pm=pm)
print("SUCCESS\n")
return True, dict(rdc=rdc, fbw=fbw, pm=pm)
def design_diffAmpP(db_n,
db_p,
sim_env,
vdd,
cload,
vincm,
T,
gain_min,
fbw_min,
pm_min,
inoiseout_std_max,
vb_p,
vb_n,
error_tol=0.05):
"""
Inputs:
Returns:
"""
# Constants
kBT = 1.38e-23 * T
# TODO: change hardcoded value
vstar_min = 0.15
# find the best operating point
best_ibias = float('inf')
best_op = None
# (loosely) constrain tail voltage
# TODO: replace with binary search
vtail_min = vincm + 2 * vstar_min
vtail_max = vdd
vtail_vec = np.arange(vtail_min, vtail_max, 10e-3)
# sweep tail voltage
for vtail in vtail_vec:
# (loosely) constrain output DC voltage
# TODO: replace with binary search
vout_min = vstar_min
vout_max = vtail - vstar_min
vout_vec = np.arange(vout_min, vout_max, 10e-3)
# sweep output DC voltage
for vout in vout_vec:
in_op = db_p.query(vgs=vincm - vtail,
vds=vout - vtail,
vbs=vb_p - vtail)
load_op = db_n.query(vgs=vout, vds=vout, vbs=vb_n - 0)
# TODO: constrain number of input devices
nf_in_min = 4
nf_in_max = 30
nf_in_vec = np.arange(nf_in_min, nf_in_max, 2)
for nf_in in nf_in_vec:
ibranch = abs(in_op['ibias'] * nf_in)
if ibranch * 2 > best_ibias:
continue
# matching NMOS and PMOS bias current
nf_load = int(abs(round(ibranch / load_op['ibias'])))
if nf_load < 1:
continue
iload = load_op['ibias'] * nf_load
ibranch_error = (abs(iload) - abs(ibranch)) / abs(ibranch)
if ibranch_error > error_tol:
continue
# create LTICircuit
amp = LTICircuit()
amp.add_transistor(in_op, 'out', 'in', 'gnd', 'gnd', fg=nf_in)
amp.add_transistor(load_op,
'out',
'gnd',
'gnd',
'gnd',
fg=nf_load)
amp.add_cap(cload, 'out', 'gnd')
num, den = amp.get_num_den(in_name='in',
out_name='out',
in_type='v')
gm = in_op['gm'] * nf_in
ro = 1 / (in_op['gds'] * nf_in + load_op['gds'] * nf_load)
# Check against gain
gain = abs(num[-1] / den[-1])
if gain < gain_min:
print("GAIN: {0:.2f} (FAIL)\n".format(gain))
continue
print("GAIN: {0:.2f}".format(gain))
# Check against bandwidth
wbw = get_w_3db(num, den)
if wbw == None:
print("BW: None (FAIL)\n")
continue
fbw = wbw / (2 * np.pi)
if fbw < fbw_min:
print("BW: {0:.2f} (FAIL)\n".format(fbw))
continue
print("BW: {0:.2f}".format(fbw))
pm, gainm = get_stability_margins(num, den)
# Check against phase margin
if pm < pm_min or isnan(pm):
print("PM: {0:.2f} (FAIL)\n".format(pm))
continue
print("PM: {0:.2f}".format(pm))
# Check against noise
inoiseout_std = np.sqrt(
4 * kBT * (in_op['gamma'] * in_op['gm'] * nf_in * 2 +
load_op['gamma'] * load_op['gm'] * nf_load * 2))
if inoiseout_std > inoiseout_std_max:
print("INOISE STD: {} (FAIL)\n".format(inoiseout_std))
continue
print("INOISE STD: {}".format(inoiseout_std))
# Check against best bias current
if ibranch * 2 < best_ibias:
biasing_spec = dict(
db_n=db_n,
db_p=db_p,
sim_env=sim_env,
vdd=vdd,
vout=vout,
vincm=vincm,
nf_in=nf_in,
nf_load=nf_load,
vtail_target=vtail,
itail_target=ibranch * 2,
iref_res=10e-9,
vb_p=vb_p,
vb_n=vb_n,
error_tol=error_tol,
)
biasing_params = design_biasing(**biasing_spec)
if biasing_params == None:
print("BIASING PARAMS (FAIL)\n")
continue
print("(SUCCESS)\n")
best_ibias = ibranch * 2
best_op = dict(
itail=best_ibias,
nf_in=nf_in,
nf_load=nf_load,
vout=vout,
vtail=vtail,
gain=gain,
fbw=fbw,
pm=pm,
nf_tail=biasing_params['nf_tail'],
nf_bias_tail=biasing_params['nf_bias_tail'],
nf_bias_in=biasing_params['nf_bias_in'],
nf_bias_loadM=biasing_params['nf_bias_loadM'],
nf_bias_load1=biasing_params['nf_bias_load1'],
iref=biasing_params['iref'],
inoiseout_std=inoiseout_std)
break
if best_op == None:
raise ValueError("No solution for P-in diffamp")
return best_op
