IDEAS to INTEGRATED CIRCUITS

      LM13600_Die_Photo

  ========RESOURCES===================

  1)   Productivity Tools
        For when getting something to work requires a little more attention to details.
      A) SPICE_HOW2_EXAMPLES with Source Code.
      B) NGSPICE_TEMPLATES 
      C) NGSPICE_SANITY_TESTS_BIPOLAR_AND_CMOS _MODELS_AND_EXPERIENCE
      D) TAPE_OUT_USING_ELECTRIC

  2 )  Frequently Used Javascript Calculators 
        Some times it is far easier to just create yourself a tool in order to save a lot of work.
     A) Recording Reverse Polish calculator
     B) R_C_F calculator
     C) R_C_L_F calculator
     D) Formula _calculator
     E) Graph_Data_Capture
     F) Table_Data_Grapher
     G) 3D_FFT_calculator
     H) Other Javascript Calculators

  3)  Cheat sheets for Analog IC Design
       An ongoing collection of  Cheat Sheets.
       Details that have been critical to past IC designs.
       And now on to  Cheat Sheets2.

  4)  Fun  Stuff
      A) Fun Pictures
      A) Fun Pictures2
      B) Fun_Documents
      C) File_Formats
      D) Manuals
      E) Other_Stuff


======INTEGRATED_CIRCUIT_STORIES==========

  1) The LM13600/LM13700  Story
          The top Die Photo is of the LM13600/13700 STEREO Transconductance Amplifier.
          Some SUPPLEMENTAL CIRCUIT EXAMPLES have been added to this web site.
          A more accurate  LM13700 SPICE model might need better transistor models.

           LM13600/stereovolume.jpg
                 
  2)  Ground Fault Interrupter Stories
        As of last shopping trip, about 50% of the GFIs found to use this Integrated Circuit.
         GFI/LevitonInStore.jpg



  3)  Some Silicon Dust Stories
       
Much smaller geometry's lead to "Silicon Dust".
       An example is the Tiny ADCV0831
which is a low power 8 bit ADC
.
         ADC0831/ADCV0831.jpg


  4) The LM383 Story
          Development of an Automotive Power Amplifier.
         LM383/LM383HookUp.jpg

  5) The LM6142 Story
          Development of an RRIO Operational Amplifier.
     LM6142/lm6142z.jpg

  6) The LMC2001 Story
          An attempt to design a PERFECT OP AMP.
          See how close First_Silicon came to being perfect.

        LMC2001/LMC2001_press2.jpg

7) The LM1991 Story
          How to design a BiCMOS/Mixed Signal IC before the invention of  BiCMOS.

     LM1991/LM1991_Block.jpg

 8) An AM STEREO Story
          National Semiconductor came out a universal AM Stereo Decoder IC before a FCC decision.
          The Data Sheet and Application notes and presented Paper for the LM1981 are included.

               AM_Stereo/AppNote.jpg



 
9) LapTop BreadBoarding.
       Use your laptop as a lab to get hands-on analog experience.
       Record/ Create/ Modify/ Control/ View/ Hear/ Etc..  Audio on your LapTop.
       A better way to hook up circuits without solder has been found.

           PlayWithFink/LapTopHow2/firstwave.jpg


  10) Build a LapTop Curve Tracer
         It only needs a RRIO quad Op Amp and a Binary counter.
         And convert the waveforms into volts and amps format.
         LapTop_CurveTracer/curvetrace.png

  11)   The File-Your-Own-Patent On-Line Story
       See what is all involved with up-loading your patent to the US Patent Office.
       The technical details to this example invention are located here.
       And the Adventure Continues if or when the application gets rejected.
       Is there an Optional Incentive Opportunity available to the US Patent System?

        USPO_Adventures/FileOnLine.jpg


  12) How to TAPE OUT a Mixed-Signal BiCMOS IC for Free.
          Just Add Time and Skill...  
       
Here is a Template File that shows how to use all the tools.
          Sometimes is might come in handy to be able to Look Inside a GDSII File.

    PlayWithICEDIT/LabelSchem.jpg


 13) The Story of the Reading Glass Ring.  
       
An ongoing effort directed at one Baby Boomer challenge.

                          MY_Patents/Reading_Ring/readring.jpg
              
  14) The Story of the Class AB Transconductance Input  
       
Do some distortion cancellation with output headroom gain.

            TaleOf2Inventions/AB_input.jpg

  15) The Story of the Transconductance Capacity Format 
       
Or how to  not have to put pre-distortion circuits in front of
          every transconductance amplfier.

                TaleOf2Inventions/PercentFormat.jpg

  16) The Story of Balanced BandGap
        
Or how two wrongs can make a right in analog IC design.
 
          BalancedBandGap/BalBandGap.jpg

  17) The Energy Harvesting Resistor
        
Turn any AC power into DC power at high efficiency without using any rectifiers.
           A pdf file version can be found here.
      Harvest_Resistor/FIG6.jpg
18)  A Fast and Simple Asynchronous Level Crossing  Analog to Digital Converter
        
This  Auto Folding Multi-bit High Speed Comparator could have been invented in the 60's.
         
  A pdf file version can be found here.


         Simple_Asynchronous_ADC/FullSchematic.jpg

19)  A  Working Bridgeless AC<=>DC PFC Converter BreadBoard
        
The prototype circuit is fully functional using analog circuity. The pdf version can be found here.

     Rectifierless%20AC%3C-%3EDC/FirstAC%3C-%3EDC.jpg
20)  An Simple BiCMOS Arduino Curve Tracer which writes data to a text file.
        
This circuit only needs a dual OpAmp and some resistors and capacitors. The pdf version can be found here.

             

21)  A Paper Zipper Method for constructing any computer 3D object out of Paper.
         
An easy method to construct  curved 3D computer objects out of paper has been found.


        



  22) Should an Engineer change his job every 5 years?
           Does technology really change that fast?
           My resume and patent portfolio perhaps reflects such a story.
           And now for some Other Stuff.





========ANALOG ART===================

1) Productivity Tools and Templates   
 
   In Electronics there always seems to be opportunity to spend time to save time.
    Some times it is far easier to just create yourself a tool in order to save a lot of work.
     A) Recording Reverse Polish calculator
     B) R_C_F calculator
     C) R_C_L_F calculator
     D) Formula _calculator
     E) 3D_FFT_calculator
     F) Other Javascript Calculators
   Getting something to work often requires far more attention to detail than the help files provide.
  Working examples need to have all the required details in place just to work.
  The following "work in progress" organized working examples intended for  cut and paste
use.
   A) macspice/winspice   Template web page
   B) SIMetrix            Template web page
   C) javascript          Template web page
   D) Perl                Template web page
   E) Ccode               Template web page
   F) Xcode               Template web page
   G) Web Page            Template web page
   H) Icarus Verilog      Template web page
   I) LabView             Template web page
   J) ICEDIT              Template web page
  
K) Quartz              Template web page
   L) MacUnix             Template web page
   M) FINK                Template web page
   N) XCircuit            Template web page
   N) Excel               Template web page
   O) AquaTerm            Template web page
   P) Dynagraph           Template web page
   Q) GnuPlot             Template web page
   R) GerberView          Template web page
   S) Mathomatic          Template web page
   T) Open Old Mac Files  Template web page
   U) SciLab              Template web page
   V) Arduino             Template web page
   W) SVG                 Template web page
   X) MS_WORD             Template web page
   Z) OCTAVE              Template web page
   The following is the second generation of template how to files.
   This version is getting bigger in size and includes  resources.
   Please note that it s starting to get impossible to avoid all forms of trouble.
   Including code and resources can help in most cases.
   A healthy ability to debug missing details looks like it is becoming a requirement.
   A) GIMP_SCRIPT               Templates, and Resources
   B) QUARTZ_JAVASCRIPT_KERNEL  Templates, and Code, and Resources
   C) PHOTOSHOP_JAVASCRIPT      Templates, and Code
   D) HTML_5                    Templates
   E) NGSPICE                   Templates
   F) ILLUSTRATOR_JAVASCRIPT    Templates
   G) GIMP_PYTHON_COPY & PASTE  Templates, and pdf and Resources

2) Free Spice
    Several free or semi-free versions of spice are available off the web.
    SIMetrix is a cadence/pspice like limited free version for  windows.
    Macspice is a spice-standard free version for OS X which allows scripting.
   
Winspice is the spice-standard free version for windows which almost works using the same code.
    This simple little PLL transient simulation runs off the exact same code.
    A simpler PLL transient simulation can be done using eight lines of Spice Code..

3) Spice Models QA
    The design engineer using a model is the really the one responsible for the model being accurate.
    Sometimes the TC of a diode needs to be sanity checked in order to design a bandgap reference.
    Matching a model to a curve tracer is typically the first thing to do.
    The extended bipolar dynamic range of today's  BiCMOS makes a Gummel Poon Plot more critical.
    The old standard bipolar transistors behaved more like this.
    Subthresshold behavior of MOS transistors should be sanity checked as well.

4) Spice Scripting
    Designing something like an Op Amp requires testing a circuit  over  all the "corners".
    Many permutations need to be tested because a design will typically fail at a subtle "corner condition".
   
The permutations typically involves 3 temperatures, 2 supply voltages, multi-applications, and several "process corners".
    A scripting ability in Spice allow the changing of its internal simulation conditions on the fly.
    This enable  a single multi dimensional simulation to effectively test everything.
    The results
can be stored in a text file which can be further processing by a perl program.
    Simulators such as Macspice/Winspice and cadence (Ocean)  and
SIMetrix(not_free) allows scripting.
    The scripting resource can be used to  do customized testing of things like THD, capacitance, and F_tau

5) BSIM4 simplified
    The latest BSIM4 manual off the web describes about 300 model parameters.
    If one downloads the following 180nm to 22nm BSIM files off the web.
    That adds up 3300 BSIM model parameters which may or not may be critical .
    It would be convenient if all the data could be reorganized as a table.
    Acrobat Pro allows the conversion of a pdf file to the following text  file which has been slightly cleaned up.
    A simple perl program can dump all the model files into a single text file.
    Another perl program can use the previous two text files to create a table of all parameters versus process.
    The table can further be color coded to view the trends.

6) PERL and text files
    Production test data for an Analog IC is usually available as a text file.
    The previous BSIM4 simplified example shows how perl can read and reorder text data such as a data log.
    This feature can also come in handy for the 
previous Spice Automatic Testing example.
    The previous perl program that combines directories into a single text file gets a lot of use.
    Another handy program can reorganize the data within a single text file.


7) The Most Beautiful Equation in the World.
    Euler identity has been described by some as "the Most Beautiful Equation in the World".
    A FFT is really just  mapping analog signal to
Euler identity.
   
This can be better seen when the results of a FFT is  plotted in 3D.
    A javascript calculator as been developed which can also do the 3D plotting.  
   

  8) Transient Noise Simulations
    Spice programs like SIMetrix allow noise to be simulated in transient analysis.
    For spice programs like Macspice/Winspice,  a RandomPWL javascript can created the data.
    SPICE can read the PWL file and simulate and  plot  both transient and spectrum results.
    Using a Noise Transient Analysis, it is possible to  see how two noise sources add together.
    Macspice allows for the creation and simulation of Arbitary Waveform Random Data.
    Some vector spice processing can show how noise adds with power.
    It is even possible to create and transient simulate 1/f noise.
    It is also possible to histogram flat noise
  and  guassian noise.

9) THD Simulation using Sprectrum Analysis
     Simulating  THD  in transient  analysis shows the  actual distorted waveforms.
     Selected elements of the spectrum output can be mathematically processed to get THD .
     The classical distortion over temperature of a differential input is a good place to start.

     Adjustments of area ratios for distortion cancellation for an alternative input can also be viewed.
     The distortion profile of differential input stages all track absolute temperature.
     Sometimes a detail look at the distortion harmonics is desirable.
     Plotting lines can be useful when looking for things like third order intercept is desirable.
     Viewing distortion that happens at either the input stage or output stage is sometimes needed

10) Extremely Easy Ways to Generate Spice Waveforms
      By making a voltage ramp that tracks time, waveforms can be generated using equations.
      Some examples are Triangle waves, Square waves, and Ramp waveforms .
      This can be extended  to making PWM waves that can also be made to be in sync .
      Equations for Amplitude Modulation and Phase modulation also work.
      But this makes it real easy to Sweep Parameters of the Input Signal over time.

11) Play with Transmission Line Reflections
      The EDN trade magazine  has written some good articles about Time-domain reflectometry.
      Modeling transmission lines as LC subcircuits may give some vision as to what is happening .
      The various impedance mismatches can be all simulated.
      The results are all the same but all internal node voltages and currents are visible.
      The cable speed appears to simply track the time constants of resonance elements.
      Identifying and tweeking out cable discontinuities can also be played with.
      The modeling of transmission lines are usually more complex.
     
12) Watch Noise Cancellation Work Inside an Op Amp.
      In negative feedback, an amplifier will try to cancel out all internal noise sources.
      A Noise Transient Analysis applied to an Amplifier can show everything working .
      Modeling an accurate Audio frequency Noise waveform can be very useful .
      Transistor subcircuits can then be modeled to have their noise properly track bias current.
      Observing how current noise can be modeled as input noise voltage is a good sanity check.
      N
oise operating in an Operational Transconductance Amplifier can also be observed.

13) Simulate a Pinch Resistor.
      A subcircuit can be made to follow the equations of a pinch resistor.

14) The Balanced Low Voltage BandGap.
      Need an accurate low voltage bandgap that works down to 900mV over temperature?
      The age old design technique of  balancing out errors still works .
      But balancing is only as good as it is possible to know all the errors.

15) State Variable Filters Map Equations to Circuit Components.
      Relating  the equations to the simple term of Q is a good starting point.
      The Q
terms in the equation  maps to feedback in State Variable Filters.
      The frequency terms map independently to the integrator terms.
      The equation works on resistor ratios and not absolute values.
     
Operational Transconductance Amplifier can replace the integrators
      This allows  voltage to control the frequency of a
State Variable Filter.
      It also allows complete IC integration of analog audio
frequency filters.
      The mapping comes in handy making Butterworth and Bessel filters

16) FFT Your Company's Stock Using Spice
      Reading a file as a PWL voltage source allow the import of REAL Input Signal.
      It only requires a spreadsheet and a text editor to input any data.
      Software is being written to  convert computers into oscilloscopes.
      A PC's line-in port can be used to digitize
Audio frequency waveforms.
      And USB hardware is being developed to digitize higher frequencies.

17) Make Some Pretty Waveforms.
      Generating Lissajous waveforms involves using the X/Y features of spice.
      Another
X/Y oscilliscope application is for BH curves.
      Lorenz Chaos and Chua Chaos can also produces some pretty curves.

18) Measure Stray Capacitance Within Spice.
      The scripting features in Spice can be used to measure and print out capacitance.
      This feature extends to measuring all the strays capacitance's within a MOS device.
      The feature further extends into making a CV plot of gate capacitance.

19) Investigate f_tau Parameters using Spice scripting.
    
Page 72 of the Gummel-Poon Toolkit describes the f-tau situation.
      Observes the effects of changing TF or CJE or IKF or ITF or VTF or XTF.
     
In MacSpice, the  unknown array  can be used to  plot  ftau versus  say TF.


20) Voltage Controlled Filters
    
State Variable filters can vary their frequency if made using gm_C stages.
      The Low Phase distortion of a Bessel filter will hold over all VCF frequencies.
      The flat pass band response for a Butterworth will hold as well.
      The Phase distortion of a Butterworth does change with VCF frequency.


21) Group Delay on Phase Distortion.
     The Bessel filter shows why good group delay means low phase distortion.
     The Butterworth filter shows the source of phase distortion.   
     MacSpice provides better ways to  observe group delay in Bessel  and Butterworth filters.

22) New Thermal Concerns.
     Silicon Oxide has one tenth the thermal conductivity of silicon.
     Oxide Isolation thermally isolates transistors.
     This simulation investigates real lab measured thermal self heating
.

23) Simple Logic Functions in Spice.
     Sometimes simple logic functions can be defined with a single spice line.
      Only ten lines of spice code are need generate a clockless ADC and DAC.
      Adding a sample and hold turns a clockless ADC into a normal ADC.
      Edge detection circuits require some timing elements.
      Convergence may require Flip Flops to have break before make timing
  
24) Interesting Effects of Distortion in Filters
      Distortion with feedback allows filter operation under multiple states
      Chaos type plots can show these effects in active filters.
      Chaos such as Chua or Lorenz could be thought of as multi dimensional instability.
      Distortion also can generate a "hang on" and "snap back" effect

25) Generating FM In Spice May Be Easy By Using PM
      Frequency Modulation in Spice is really Phase Modulation
      And  Phase Modulation is really Double Frequency Modulation.
      An alternative way of generating a FM signal is through PM
      This allows FM or PM to be done in a Piece Wise Linear Fashion.
      Or  view an  FM Spectrum  as a Polar to Rectangular Conversion.
      The FM Spectrum can be fully visualized in this way.

26) Automotive Power Amplifier Design
      How a Full Automotive Amplifier was built using only 5 leads
      The AB_Bias versus CrossOver Distortion tradeoffs.
      Bottom side output stage saturation and top side hang on.
      Bottom side Fuzzies.
      Why the short lead rule.
      Top side composite stablity and the Invention that addresses it.
      Chrysler thermal shut down problem.
      Output transistor IR drop and transistor layout.

27) An AB_Biased Operational Transconductive Input Stage
    
It is possible to lower noise and offset while also lowering distortion.
      A differential Bipolar Input stage's distortion tracks absolute temperature.
      A dual differential Bipolar Input stage can reduce distortion.
      The distortion of a dual differential Bipolar Input stage  also tracks absolute temperature.
      A new AB_Biased Input has adjustable cross over distortion.
      And it has an adjustable current gain over its DC current.
      And the distortion also tracks absolute temperature.
      To compare to a LM3080 architecture, offset, distortion and noise needs to be simulated.
      The comparision is made by putting the AB_Biased input stage in a  LM3080 application.

28) Plotting a Root Locus Using Spice
      Spices's  Pole/Zero analysis can be sanity checked against a plotted a Root Locus.

29) Bipolar and CMOS Noise Parameters
      An attempt to match the Noise Voltage and Noise Current of a LM394 .
      The Noise voltage for a BiCMOS NPN is as expected.
      But 1/f Noise for a CMOS transistor may be getting interesting.

30) Bipolar RRIO Operational Amplifier Design
      The LM324 leads to the RRIO Op Amps.
      Bipolar input requirements and Supply Voltage.
      Preferred input steering and using vertical pnps.
      The need for input clamp diodes.
      A clamp to slew rate invention.
      An AB Bias Dual Input Turnaround.
      Shortening the signal path.
      Balancing out beta loading.
      GraceFull death at the output stage.
      Shortening the signal path at the output.
      Saturation current limit.

31) A Perfect  RRIO Operational Amplifier Design 
      Chopper Amplifiers frequency shifts both offset and 1/f noise.
      This however can lead to an input aliasing problem.
      The aliasing problem is commonly fixed using spread spectrum.
      An FM limiter gain stage shows how to take a lot of gain.
      This same gain can be done using an on chip capacitor.
      The DC offset is cancelled out using a subHertz integerator.
      The chopper signal gain stage tends to remove offset and 1/f noise anyway.
      A similar gain stage can be used to quietly spreadspectrum an oscillator.  
      If the chopper signal is integrated, it becomes a low frequency precision Op Amp.
      This precision Op Amp can extend the gain of  another Op Amp
      Together the two Op Amps can compose a composite Op Amp.
      An the composite Op can bury both offset and noise.
      It may also be possible to reduce noise input current as well.

32) Different Spectrum Formats 
      Using the Euler Format may be the most precise.
      But SPICE may need to use a different format.
      The format  MacSpice  uses is as such.
      Spectrums can and may need to be formatted as pure AM or PM.

33) Simple Math Processing in SPICE     
      Things like a  RMS value can be calculated from any waveform.
      Specific points in a spectrum can be printed out.
      A spectrum printout  may be required to see AM from PM sidebands.

34) Jitter Analysis in SPICE 
       Jitter analysis can show edge timing over time.
       But Jitter involves a process of accumulating random timing error.
       And accumulated random noise accumulates error with time.

35) Pulse Width Modulation without Phase Modulation?
      Spectrum analysis  says that a balanced PWM has no Phase shift.
      A bandpass filter and  an inverter verifies that fact.
      Jitter Analysis shows how jitter can happen with zero Phase shift.

36) Some Noise Surprises in Transient Analysis
      The difference between rms  and magnitude can create confusion.
      How to lower the bandwidth of noise while keeping the same rms.

37) Oscillator Phase Noise in Transient Analysis
      Import  a noise file into a free running oscillator's spectrum.
      Export jitter from a noisy free running oscillator.
      Phase modulate  a  signal to  match a free running oscillator's spectrum.
      Predict  how white  noise will appear on a free running oscillator's spectrum.
      An even better discussion can be found here and also here.    

38) Mathematically process SPICE's Output waveforms within Spice.
      Extract and plot prop delays vs supply voltage applied to CMOS inverters.
      Extracted and average time periods to precisely measure a crystal oscillator's frequency.
      The frequency of a crystal can be mathematically extrapolate from an AC simulation.
      How a varactor can vary the frequency of crystal oscillator can be precisely measured.
      Removing SPICE's phase wrap around can makes viewing a crystal's phase easier.

39) Digital filter simulations using behavioral models in Spice.
      A behavioral model to meet the need for a two phase clock.
      Behavioral Models using switches show the theoretical limitations.
      Two phase clock switching of a capacitor behaves like resistors.
      Two sample and hold stages makes an analog delay element.
      Analog delay elements are the basic building blocks in digital filters.
      Low pass filters average what happens in the past with the present.
      High pass filter compare differences between the past and present.
      Delayed analog signals in feed back behave like analog filters.

40) Eye Diagram Simulation resources in Spice.
      Spice has the resources to plot a Eye Diagram using random digital signals.
      Digital randomness can be done digitally or linearly.
      Viewing how an Eye Diagram is actually being degraded can be be intuitive.
       The BER requirements need to be considered.

41) Different architectures for CMOS current mirrors.
      How does a pure cascode CMOS current mirror compare to a BiCMOS mirror?
      Some mirrors use CMOS transistors like degeneration resistors.
      A self cascode architecture has its features as well.

42) Perfect Logic versus Real Logic in SPICE.
      Using Behavioral Logic in most cases does not present a problem.    
      Some Behavioral Flip-Flops will converge if care is taken to hold all inputs stationary.
      A Behavioral Flip-Flop used in a counter application may require break before make to converge.
      Building Phase Frequency detectors may need this feature to converge,

43) Load Sweeping Transient Analysis.
      Sometimes it might be useful to sweep the load current of a Charge Pump over a large dynamic range.
      Sweeping the load current with time can verify the output impedance of a Voltage Multiplier.  

44) Duty Cycle Sweeping Transient Analysis.
      Transient analysis can provide an easy to graph the Output of a Buck Converter versus Duty Cycle.
       Output Voltage versus Duty Cycle versus Output Resistance can be plotted for a Buck Converter .
       The same can be done for a Boost Converter, a Boost Buck Converter , and a SEPIC Converter.

45) More Spice Features
       Having working examples of what all the Waveform processing function do leaves nothing out.
       The waveform Sort Function is powerful but not straight forward on how to use it.
       Transient timing is not  consistent  for things like square waves.
       Sine waves that are sampled close to nyquist appear to have an attentuation compared to normal.
       Piece Wise Linear wave forms have inconsistent timing which can be fixed with a linearize statement.
       If a version of Spice has funny blanking for X/Y plots, it is due to the curve tracer application
       It is possible to build an Arbitrary WaveForm Generator in SPICE.
       ============SOURCE CODE FOR ABOVE=======================

46) FFT Windowing Fun
       Windowing divides up signal into time frames while reducing Spectrum Leakage at the same time.
       Windowing typically converts a sine wave into  a Classical AM spectrum located at three frequency bins.
       The Spectrum leakage is reduced when input signal is converted  into Window Distortion Harmonics.
       Sometimes adding 2nd and 3rd harmonic distortion to the window can reduce Spectrum leakage.
       Testing of all the Windowing functions  can be automated.
       There are ways to plot all of the Windowing function results  on a single plot.
       ============SOURCE CODE FOR ABOVE=======================

47) New FFT/IFFT Functions for MacSpice
       The New FFT/IFFT functions appear to operate in both a Euler format and a Frequency format.
       Some attention needs to be placed on having consistent timing in the waveform.
       A normal square wave has some timing details that should be addressed.
       Adjustments in timing can fix Spectrum leakage.
       Triangle waves work as expected.
       Sine waves can show the limits to precision.
       Spectrum leakage can be view as a waveform.
       Butterworth filters can now be better tested for group delays.
       Bessel filters can now be better tested for group delays.
       Input distortion can now be extracted and viewed is a waveform.
       Output distortion can now be extracted and viewed is a waveform.
       ============SOURCE CODE FOR ABOVE=======================

48) Redefining Ohm's Law
       Where is energy lost in a Full Wave Rectifier?
       Where is energy lost in Switched Capacitors?
       Where is energy lost in Switched Supplies?
       Class D output stages as found in audio.
       A Class D Op Amp.
       Building a Current Source using Feedback.
       A Class D Current Source.
       A Dual Supply Class D output stage.
       A Class D Resistor and Ohm's Law
       The Energy Harvesting Resistor.
       ============SOURCE CODE FOR ABOVE=======================

49) Randomness for Better or Worst
       When you take N samples,  how well  can you trust the result?
       A random transient simulation is easy to do in spice.
       A random transient simulation can demonstrate noise adding with power.
       Digital randomness is repeatable, which makes it quite useful.
       How low does a standard deviation need to be for a given Bit error rate?
       It is easy to generate a random stream of ones and zeros.
       Undersampling noise only packages the same RMS power into less bandwidth.
       Accumulated noise is different from normal randomness.
       A jitter transient simulation can be done in spice.
       A transient eye chart simulation shows the impact of cable limited bandwidth.
       Personally modeling a cable may be much more trust worthy in the end.
       The spectrum for a simple AM signal shows the spectrum's scaling.
       The spectrum for a simple PM signal attempts to match that of a AM signal.
       Phase modulation by a random signal has a predictable spectrum.
       Phase modulation by accumulated noise maps nicely to the PM noise spectrum.
       Only ten lines of spice code are need generate a clockless ADC and DAC.
       Adding a sample and hold turns a clockless ADC into a normal ADC.
       Spread Spectrum Sampling for ADCs spreads out all harmonics.
       A Spread Spectrum Sampled ADC  (SSS) does not alias.
       Quantization error was a problem for early digital audio.
       The dithering technique solved the Quantization error  problem.
       ============SOURCE CODE FOR ABOVE=======================

50) Can this be a Simple way to predict Oscillator Phase Noise?
       How can a Graph and a Calculator predict Phase Noise? 
       How does the accumulation of Phase Noise Work?
       How much does Low Phase Noise Cost?  
       How does supply voltage effect Phase Noise? 
       How does Phase Modulation resembles Amplitude Modulation?  
       How does Noise gets spread out during sampling?  
       How does Noise react to under sampling?  
       How can a random PM spectrum can be easily predicted?  
       How does a tuned circuit's bandwidth really equal frequency over Q?  
       ============SOURCE CODE FOR ABOVE=======================

51) DC controlled Spice Subcircuits to make Universal Analog/Digital Filters
       Transient simulating a DC controlled Universal Analog Filter Block.
       Demonstration how to DC control the filter type of a Universal Analog Filter.
       Demonstration how a Digital "z" block can work like an Analog "s" block.
       Substituting and running  "z" for "s" blocks  in the same circuit .
       Classical Brickwall filter approximations using analog filter blocks.
       Using FFT/IFFT to  simulate a perfect Brickwall filter on a square wave.
       Using FFT/IFFT to  simulate a perfect Brickwall filter's impulse response.
       DC applying a perfect Brickwall filter's impulse response to a FIR Digital filter.
       Demonstrating how a FIR with Brickwall filter's impulse response filters correctly. 
       How a Phase shifting Hilbert filter is needed for single sideband transmission.  
       DC controlling a 6 pole ALLPASS to be a have linear frequency to phase shift.
       Using two 6 pole ALLPASS filters to create two outputs which have 90 degrees of offset.
       Using FFT/IFFT to simulate a Hilbert Filter applied to a square wave.
       Using FFT/IFFT to simulate impulse response of a Hilbert Filter.
       DC applying a impulse response of a Hilbert  to a FIR Digital filter.
       Demonstrating how a FIR with the impulse response of a Hilbert  filters correctly.
       ============SOURCE CODE FOR ABOVE=======================

52) Delta Modulation and Sigma Delta, etc...
       Reinventing Delta Modulation, and some background history.
       Sigma Delta and Noise Shaping transient and FFT spice simulation.
       Second order Sigma Delta and Noise Shaping transient and FFT spice simulation.
       A spice simulation that demonstrates how OverSampling works.
       Doing spice transient and FFT simulation of Decimation.
       A digital filter spice simulation which demonstrates Interpolation.
       ============SOURCE CODE FOR ABOVE=======================

53) Analog to Digital Conversion using (when something happens) Event Sampling
       Reading about Folding ADCs turned up an easy architecture to perform the same function
       Folding and Flash architectures have been around for some time, but none this simple.
       Asynchronous Analog to Digital Conversion using Level Crossing definitely follows different rules
       When Asynchronous Analog to Digital Conversion is sampled with a clock, things return to normal
       Initially, Threshold Sampling look like it is truncating data.
       An easy extrapolation method is shown here, and more advanced methods are found here.
       Extrapolation actually works quite well even using simple methods.
       Adding some Additional Event Sampling to Threshold Sampling can greatly enhance full signal capture.
       ============SOURCE CODE FOR ABOVE=======================


      When we remember we are all mad, the mysteries disappear and life stands explained.  - Mark Twain

       Any fool can criticize, condemn and complain,  and most fools do. - Ben Franklin
                                                                                                               
       Your worth consists in what you are and not in what you have. - Thomas Edison

       You may fail many times, but you are still not a failure until you begin to blame someone else.  ????

       The most exciting phrase to hear in science, the one that heralds the most discoveries, is not ‘Eureka!’
       but ‘That’s funny…’”                                                            — Isaac Asimov

                                                                                                              

      Don Sauer... DSauerSanJose@Aol.com