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-Perform Monte Carlo simulation in ngspice
-* 25 stage Ring-Osc. BSIM3 with statistical variation of various model parameters
-* cd into ngspice/examples/Monte_Carlo
-* start in interactive mode 'ngspice MC_ring.sp' with several plots for output
-* or start in batch mode, controlled by .control section (Control mode)
-* with 'ngspice -b -r MC_ring.raw -o MC_ring.log MC_ring.sp'.
-
-vin in out dc 0.5 pulse 0.5 0 0.1n 5n 1 1 1
-vdd dd 0 dc 3.3
-vss ss 0 dc 0
-ve sub 0 dc 0
-vpe well 0 dc 3.3
-
-.subckt inv1 dd ss sub well in out
-mn1 out in ss sub n1 w=2u l=0.35u as=3p ad=3p ps=4u pd=4u
-mp1 out in dd well p1 w=4u l=0.35u as=7p ad=7p ps=6u pd=6u
-.ends inv1
-
-.subckt inv5 dd ss sub well in out
-xinv1 dd ss sub well in 1 inv1
-xinv2 dd ss sub well 1 2 inv1
-xinv3 dd ss sub well 2 3 inv1
-xinv4 dd ss sub well 3 4 inv1
-xinv5 dd ss sub well 4 out inv1
-.ends inv5
-
-xinv1 dd ss sub well in out5 inv5
-xinv2 dd ss sub well out5 out10 inv5
-xinv3 dd ss sub well out10 out15 inv5
-xinv4 dd ss sub well out15 out20 inv5
-xinv5 dd ss sub well out20 out inv5
-xinv11 dd 0 sub well out buf inv1
-cout buf ss 0.2pF
-*
-.options noacct
-.control
- save buf $ we just need buf, save memory by more than 10x
- let mc_runs = 30 $ number of runs for monte carlo
- let run = 0 $ number of actual run
- set curplot = new $ create a new plot
- set curplottitle = "Transient outputs"
- set plot_out = $curplot $ store its name to 'plot_out'
- set curplot = new $ create a new plot
- set curplottitle = "FFT outputs"
- set plot_fft = $curplot $ store its name to 'plot_fft'
- set curplot = new $ create a new plot
- set curplottitle = "Oscillation frequency"
- set max_fft = $curplot $ store its name to 'max_fft'
- let mc_runsp = mc_runs + 1
- let maxffts = unitvec(mc_runsp) $ vector for storing max measure results
- let halfffts = unitvec(mc_runsp)$ vector for storing measure results at -40dB rising
-*
-* define distributions for random numbers:
-* unif: uniform distribution, deviation relativ to nominal value
-* aunif: uniform distribution, deviation absolut
-* gauss: Gaussian distribution, deviation relativ to nominal value
-* agauss: Gaussian distribution, deviation absolut
- define unif(nom, var) (nom + (nom*var) * sunif(0))
- define aunif(nom, avar) (nom + avar * sunif(0))
- define gauss(nom, var, sig) (nom + (nom*var)/sig * sgauss(0))
- define agauss(nom, avar, sig) (nom + avar/sig * sgauss(0))
-*
-* We want to vary the model parameters vth0, u0, tox, lint, and wint
-* of the BSIM3 model for the NMOS and PMOS transistors.
-* We may obtain the nominal values (nom) by manually extracting them from
-* the parameter set. Here we get them automatically and store them into
-* vectors. This has the advantage that you may change the parameter set
-* without having to look up the values again.
- let n1vth0=@n1[vth0]
- let n1u0=@n1[u0]
- let n1tox=@n1[tox]
- let n1lint=@n1[lint]
- let n1wint=@n1[wint]
- let p1vth0=@p1[vth0]
- let p1u0=@p1[u0]
- let p1tox=@p1[tox]
- let p1lint=@p1[lint]
- let p1wint=@p1[wint]
-
-*
-* run the simulation loop
- dowhile run <= mc_runs
- * run=0 simulates with nominal parameters
- if run > 0
- setplot $max_fft
- altermod @n1[vth0] = gauss(n1vth0, 0.1, 3)
- altermod @n1[u0] = gauss(n1u0, 0.05, 3)
- altermod @n1[tox] = gauss(n1tox, 0.1, 3)
- altermod @n1[lint] = gauss(n1lint, 0.1, 3)
- altermod @n1[wint] = gauss(n1wint, 0.1, 3)
- altermod @p1[vth0] = gauss(p1vth0, 0.1, 3)
- altermod @p1[u0] = gauss(p1u0, 0.1, 3)
- altermod @p1[tox] = gauss(p1tox, 0.1, 3 )
- altermod @p1[lint] = gauss(p1lint, 0.1, 3)
- altermod @p1[wint] = gauss(p1wint, 0.1, 3)
- end
- tran 15p 100n 0
-* select stop and step so that number of data points after linearization is not too
-* close to 8192, which would yield varying number of line length and thus scale for fft.
-*
-* We have to figure out what to do if a single simulation will not converge.
-* There is the variable 'sim_status' which is set to 1 if the simulation
-* fails with ’xx simulation(s) aborted’, e.g. because of non-convergence.
-* Then we might skip this run and continue with a new run.
-*
- echo Simulation status $sim_status
- let simstat = $sim_status
- if simstat = 1
- if run = mc_runs
- echo go to end
- else
- echo go to next run
- end
- destroy $curplot
- goto next
- end
-
- set run ="$&run" $ create a variable from the vector
- set mc_runs ="$&mc_runs" $ create a variable from the vector
- echo simulation run no. $run of $mc_runs
- set dt = $curplot
- * save the linearized data for having equal time scales for all runs
- linearize buf $ linearize only buf, no other vectors needed
- destroy $dt $ delete the tran i plot
- set dt = $curplot $ store the current plot to dt (tran i+1)
- setplot $plot_out $ make 'plt_out' the active plot
- * firstly save the time scale once to become the default scale
- if run=0
- let time={$dt}.time
- end
- let vout{$run}={$dt}.buf $ store the output vector to plot 'plot_out'
- setplot $dt $ go back to the previous plot (tran i+1)
- fft buf $ run fft on vector buf
- destroy $dt $ delete the tran i+1 plot
- let buf2=db(mag(buf))
- * find the frequency where buf has its maximum of the fft signal
- meas sp fft_max MAX_AT buf2 from=0.1G to=0.7G
- * find the frequency where buf is -40dB at rising fft signal
- meas sp fft_40 WHEN buf2=-40 RISE=1 from=0.1G to=0.7G
- echo
- echo
- * store the fft vector
- set dt = $curplot $ store the current plot to dt (spec i)
- setplot $plot_fft $ make 'plot_fft' the active plot
- if run=0
- let frequency={$dt}.frequency
- end
- let fft{$run}={$dt}.buf $ store the output vector to plot 'plot_fft'
- * store the measured value
- setplot $max_fft $ make 'max_fft' the active plot
- let maxffts[{$run}]={$dt}.fft_max
- let halfffts[{$run}]={$dt}.fft_40
- let run = run + 1
- label next
- reset
- end
-***** plotting **********************************************************
-if $?batchmode
- echo
- echo Plotting not available in batch mode
- echo Write linearized vout0 to vout{$mc_runs} to rawfile $rawfile
- echo
- write $rawfile {$plot_out}.allv
- rusage
- quit
-else
- setplot $plot_out
- plot vout0 ylabel 'RO output, original parameters' $ just plot the tran output with nominal parameters
- setplot $plot_fft
- settype decibel ally
- plot db(mag(ally)) xlimit .1G 1G ylimit -80 10 ylabel 'fft output'
-*
-* create a histogram from vector maxffts
- setplot $max_fft $ make 'max_fft' the active plot
- set startfreq=400MEG
- set bin_size=5MEG
- set bin_count=20
- compose xvec start=$startfreq step=$bin_size lin=$bin_count $ requires variables as parameters
- settype frequency xvec
- let bin_count=$bin_count $ create a vector from the variable
- let yvec=unitvec(bin_count) $ requires vector as parameter
- let startfreq=$startfreq
- let bin_size=$bin_size
- * put data into the correct bins
- let run = 0
- dowhile run < mc_runs
- set run = $&run $ create a variable from the vector
- let val = maxffts[{$run}]
- let part = 0
- * Check if val fits into a bin. If yes, raise bin by 1
- dowhile part < bin_count
- if ((val < (startfreq + (part+1)*bin_size)) & (val > (startfreq + part*bin_size)))
- let yvec[part] = yvec[part] + 1
- break
- end
- let part = part + 1
- end
- let run = run + 1
- end
-
- * plot the histogram
- set plotstyle=combplot
- plot yvec-1 vs xvec xlabel 'oscillation frequency' ylabel 'bin count' $ subtract 1 because we started with unitvec containing ones
-
- * plot simulation series
- set plotstyle=linplot
- let xx = vector(mc_runsp)
- settype frequency maxffts
- plot maxffts vs xx xlabel 'iteration no.' ylabel 'RO frequency'
-
-* calculate jitter
- let diff40 = (vecmax(halfffts) - vecmin(halfffts))*1e-6
- echo
- echo Max. jitter is "$&diff40" MHz
-end
- rusage
-.endc
-********************************************************************************
-.model n1 nmos
-+level=8
-+version=3.3.0
-+tnom=27.0
-+nch=2.498e+17 tox=9e-09 xj=1.00000e-07
-+lint=9.36e-8 wint=1.47e-7
-+vth0=.6322 k1=.756 k2=-3.83e-2 k3=-2.612
-+dvt0=2.812 dvt1=0.462 dvt2=-9.17e-2
-+nlx=3.52291e-08 w0=1.163e-6
-+k3b=2.233
-+vsat=86301.58 ua=6.47e-9 ub=4.23e-18 uc=-4.706281e-11
-+rdsw=650 u0=388.3203 wr=1
-+a0=.3496967 ags=.1 b0=0.546 b1=1
-+dwg=-6.0e-09 dwb=-3.56e-09 prwb=-.213
-+keta=-3.605872e-02 a1=2.778747e-02 a2=.9
-+voff=-6.735529e-02 nfactor=1.139926 cit=1.622527e-04
-+cdsc=-2.147181e-05
-+cdscb=0 dvt0w=0 dvt1w=0 dvt2w=0
-+cdscd=0 prwg=0
-+eta0=1.0281729e-02 etab=-5.042203e-03
-+dsub=.31871233
-+pclm=1.114846 pdiblc1=2.45357e-03 pdiblc2=6.406289e-03
-+drout=.31871233 pscbe1=5000000 pscbe2=5e-09 pdiblcb=-.234
-+pvag=0 delta=0.01
-+wl=0 ww=-1.420242e-09 wwl=0
-+wln=0 wwn=.2613948 ll=1.300902e-10
-+lw=0 lwl=0 lln=.316394 lwn=0
-+kt1=-.3 kt2=-.051
-+at=22400
-+ute=-1.48
-+ua1=3.31e-10 ub1=2.61e-19 uc1=-3.42e-10
-+kt1l=0 prt=764.3
-+noimod=2
-+af=1.075e+00 kf=9.670e-28 ef=1.056e+00
-+noia=1.130e+20 noib=7.530e+04 noic=-8.950e-13
-**** PMOS ***
-.model p1 pmos
-+level=8
-+version=3.3.0
-+tnom=27.0
-+nch=3.533024e+17 tox=9e-09 xj=1.00000e-07
-+lint=6.23e-8 wint=1.22e-7
-+vth0=-.6732829 k1=.8362093 k2=-8.606622e-02 k3=1.82
-+dvt0=1.903801 dvt1=.5333922 dvt2=-.1862677
-+nlx=1.28e-8 w0=2.1e-6
-+k3b=-0.24 prwg=-0.001 prwb=-0.323
-+vsat=103503.2 ua=1.39995e-09 ub=1.e-19 uc=-2.73e-11
-+rdsw=460 u0=138.7609
-+a0=.4716551 ags=0.12
-+keta=-1.871516e-03 a1=.3417965 a2=0.83
-+voff=-.074182 nfactor=1.54389 cit=-1.015667e-03
-+cdsc=8.937517e-04
-+cdscb=1.45e-4 cdscd=1.04e-4
-+dvt0w=0.232 dvt1w=4.5e6 dvt2w=-0.0023
-+eta0=6.024776e-02 etab=-4.64593e-03
-+dsub=.23222404
-+pclm=.989 pdiblc1=2.07418e-02 pdiblc2=1.33813e-3
-+drout=.3222404 pscbe1=118000 pscbe2=1e-09
-+pvag=0
-+kt1=-0.25 kt2=-0.032 prt=64.5
-+at=33000
-+ute=-1.5
-+ua1=4.312e-9 ub1=6.65e-19 uc1=0
-+kt1l=0
-+noimod=2
-+af=9.970e-01 kf=2.080e-29 ef=1.015e+00
-+noia=1.480e+18 noib=3.320e+03 noic=1.770e-13
-.end