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In a recent post titled Simulating the Knowm M-MSS Memristor Model Pulse Response with Qucs-S and Xyce, I presented circuit simulations that focus on the dynamic behavior of the M-MSS model’s incremental conductance response to applied square wave pulses. In this post I will continue to explore this behavior by creating basic logic cicuits (i.e. 2-input AND, 2-input OR gates) and perform simulations using discrete memristor elements and sub-circuit models which implement neuromemristive synapses (i.e. AHaH kT-Synapses). I will demonstrate how to configure mixed mode simulations using a 2-output pattern generator contained in the Qucs-S Xyce Digital library to configure square wave pulses with specific pulse timing to produce the truth table inputs to the logic circuits. As part of this tutorial we will also be exploring some additional advanced features of Qucs-S and Xyce for displaying timing diagrams and measuring the power across the memristor elements during the transient simulation. The new Knowm_AHaH library included in the latest release candidate #3 of the Knowm OSS EDA Stack provides AHaH synapse node configurations implemented as sub-circuits to simplify building netlists for simulating the same basic logic circuits designed using discrete memristor components. This new library will be used in future simulations of neuromemristive circuits and machine learning algorithms in hardware.

An example Qucs-S project has been created to perform various experiments that we will later set up on actual memristor devices using the Knowm Memristor Discovery board and associated extender modules. The following experiments are included in the example Qucs-S project AHaH_Logic_prj available in the examples_knowm_oss-eda-0.0.19s-rc3 bundle.

Memristor Experiments Included in the Accompanying Examples

  • ahah_mr_AND2_pl2

    (2) Rectangular Pulse sources with positive pulse amplitude of 1V with transient analysis simulating an AHaH 1-2 synapse using discrete memristor elements configured to produce the logic states of a 2-input AND gate.

  • ahah_mr_AND2

    Xyce 2-output pattern generator with positive pulse amplitude of 1V with transient analysis simulating an AHaH 1-2 synapse using discrete memristor elements configured to produce the logic states of a 2-input AND gate.

  • ahah_mr_OR2

    Xyce 2-output pattern generator with positive pulse amplitude of 1V with transient analysis simulating an AHaH 1-2 synapse using discrete memristor elements configured to produce the logic states of a 2-input OR gate.

  • ahah1-2_synapse_AND2

    Xyce 2-output pattern generator with positive pulse amplitude of 1V with transient analysis simulating an AHaH 1-2 synapse using the AHaH 1-2 synapse subcircuit configured to produce the logics state of a 2-input AND gate.

  • ahah1-2i_synapse_OR2

    Xyce 2-output pattern generator with positive pulse amplitude of 1V with transient analysis simulating an AHaH 1-2 synapse using the AHaH 1-2i (inverted) synapse subcircuit configured to produce the logic states of a 2-input OR gate.

NOTE: We will be covering the AND2 examples and the AHaH 1-2i Synapse OR2 circuit in this tutorial. The other OR2 circuits are almost identical and can be explored using the same steps as presented here for the corresponding AND2 circuits.

Prerequisites

NOTE: The instructions there should be almost identical to the ones necessary for installing release candidate #3 used for this tutorial.

  • Update to the latest release candidate #3 of the Knowm OSS EDA Stack. It is available for macOS 10.12 Sierra and Ubuntu 16.04 LTS (Xenial Xerus). This post covers installation and use on macOS and support for Xyce (Serial) simulations only. The included versions of Qucs-S (0.0.19S) and Xyce 6.6 include libraries for amd64 architectures. Support for other architectures and operating systems are under development and will be released when available.

Download and install the latest release candidate #3 from these links.

MacOS Sierra 10.12 QUCs
MacOS Sierra 10.12 Knowm Examples
MacOS Sierra 10.12 Xyce

Linux QUCs
Linux Knowm Examples
Linux Xyce

Overview

The following discussion of simulation of memristor logic circuits was developed based on the results of a paper presented by Frey, et. al. titled: “Investigating Power Characteristics of Memristor-based Logic Gates and Their Applications in a Security Primitive”. You may want to review this paper before or concurrently while working through this tutorial. The following configurations are the inspiration for the circuits we have configured here.

memristor_logic_circuits

Memristor Logic Circuits

  • We will also be using AHaH nodes which will be introduced in a following section. The basic configuration of the AND and OR gate presented use the AHaH 1-2 configuration.
    ahah_mr_logic_gates

    AHaH Logic Gates Based on Memristor Pairs

Open the AHaH Discrete Memristor AND2 Schematic diagram

  1. Double click the AHaH_Logic_prj to automatically open the Content tab.

  2. Select the ahah_mr_AND2_2pl.sch from the Schematics list in the Contents tab of the Main Dock.

    qucs_sch_ahah_mr_and2_2pl

    AHaH Memristor AND2 with Rectangle Pulses

    NOTE: We are using the AHaH 1-2 synapse AND configuration from the diagram above and the .Model directive MRM5, and the M-MSS model from the Knowm_Memristor_Technology library has been assigned for both the MR1 and MR2 memristor symbols. We have increased the ratio for the Ron and Roff parameter values in the models as discussed in the Frey paper in order to the minimum and maximum values as measured at the output voltage across the divider network.

    qucs_sch_ahah_mr_and2_2pl_mr1_mr2

    AHaH Memristor 1-2 Configuration

Pulse Voltage Source properties

  1. Double click V1 symbol on the schematic to open the parameters and review the settings for the Rectangle pulse source.

    qucs_sch_ahah_mr_and2_2pl_v1_sel

    Select V1 Pulse Source

  2. Select the U row in the properties table.

  3. The voltage is set to 1 V so the output will be from 0V to 1V.

  4. Select the TH row in the properties table determine the time duration of the high pulses.

  5. We’ve set this value to 10 ms to specify a 10 ms pulse width.

  6. Similarly the TL row in the properties table determine the time duration of the low pulses. I have set this also to 10 ms to specify a 20ms period.

    qucs_sch_ahah_mr_and2_2pl_v1_set

    V1 Pulse Source Settings

  7. Click Apply to set the frequency value.

  8. Click OK to exit the properties dialog.

  9. Similarly you can double click V2 symbol on the schematic to open the parameters and review the settings for second the Rectangle pulse source.

    qucs_sch_ahah_mr_and2_2pl_v2_sel

    Select V2 Pulse Source

NOTE: The parameters for V2 are set to be half of the period of V1. This will give us twice the number of pulses on the input of the memristor MR2 and allow use to generate the truth table for the gate inputs.

Other Schematic Components

  1. We have configured two current probes named Pr1 and Pr2 that are used to measure the current flowing through each memristor as the pulses are applied to the circuit.

  2. There are also the Name nodes w1 and w2 which will provide the voltage measured across the two memristors MR1 and MR2 respectively and represent the change of the weights and the memristor states based on the change in the conductance in each branch of the synapse.

  3. The out named node provides the positive voltage for the voltage divider at the junction of the MR1 amd MR2 memristors which defines the logic state of the synapse which should should 0 V or 1 V at the maximum pulse values.

Transient Simulation Settings

  1. Double click on the transient simulation symbol to open the setup parameters dialog.

  2. I have entered 20 ms in the stop field to coincide with the settings for the rectangle pulse sources total period.

  3. Entering 101 in the number value field to set a 200 us step size.

    qucs_sim_tran_20ms_set

    Transient Simulation Settings

  4. Click Apply to save the changes.

  5. Click OK to exit the properties dialog.

    qucs_sch_ahah_mr_sims_tran

    Transient Simulation Parameters

Save the Schematic Diagram File

  1. The filename ahah_mr_AND2_2pl.sch has been used for this example schematic.

  2. Click the Save button on the toolbar to save the schematic file.

    qucs_toolbar_save

    Save Toolbar Button

Run a Simulation

  1. Press F2 or select Simulate button on the toolbar.
    qucs_toolbar_run

    Run Simulation Toolbar Button

  2. Check simulation for errors or warnings. See the status bar at the bottom of the Qucs window lower right corner.

  3. Click the Exit button to close the Simulation window.

View the Tabular Results

  1. Check the Tabular results.

    qucs_sch_ahah_mr_and2_2pl_vt_tab

    Tabular Results

Cartesian Plot of Memristor-based AND2 Gate ( V vs. Time ) Results

  1. You should also observe the results in the specified Cartesian plot defined in the schematic.

    qucs_sch_ahah_mr_and2_2pl_vt_plot

    Voltage Inputs, Ouput vs. Time

    NOTE: The results contain multiple pulses of the 1V amplitudes for w1 and w2 we defined in the Rectangle Pulse settings. This provides the 4 states of the AND gate for the following truth table.

    ahah_and2_truth_tab

    AND2 Circuit Truth Table

  2. In the first 5 ms both p1 and p2 are positive 1 V so the out state is also positive 1 V or logic 1.

    qucs_sch_ahah_mr_and2_2pl_vt_plot_s1

    First Logic State ( 0 – 5ms )

  3. In the next 5 ms both p1 is positive 1 V but p2 is 0V so the out state is 0 V or logic 0.

    qucs_sch_ahah_mr_and2_2pl_vt_plot_s2

    Second Logic State ( 5ms – 10ms )

  4. In the next 5 ms both p1 is 0 V but p2 is 1 V so the out state is still 0 V or logic 0.

    qucs_sch_ahah_mr_and2_2pl_vt_plot_s3

    Third Logic State (10ms – 15ms)

  5. In the last 5 ms both p1 and p2 are positive 0 V so the out state is also positive 0 V or logic 0.

    qucs_sch_ahah_mr_and2_2pl_vt_plot_s4

    Fourth Logic State (15ms – 20ms)

Open the Schematic diagram

  1. Double click the AHaH_Logic_prj to automatically open the Content tab.

  2. Select the ahah_mr_AND2.sch from the Schematics list in the Contents tab of the Main Dock.

    qucs_sch_ahah_mr_and2_2pat_comp

    AHaH 1-2 AND2 Schematic

    NOTE: Again we are using is the AHaH 1-2 synapse AND configuration from the diagram above and the .Model directive MRM5, the M-MSS model from the Knowm_Memristor_Technology library has been assigned for both the MR1 and MR2 memristor symbols.

    qucs_sch_ahah_mr_and2_2pat_pg

    AHaH 1-2 Logic AND Configuration

Configure the 2-Pattern Pulse Gererator Voltage Source

  1. The PATGENX2 was added to replace the 2 rectangle pulse sources in the schematic. This is a component found in the Xyce Digital library components list.

    qucs_lib_xyce_digital_patgenx2

    Xyce 2-ouput Pattern Gen

  2. Double click PG symbol on the schematic to open the parameters and review the settings for the PATGENX2 pulse generator source.

    NOTE: The definition of the component specifies the x2 source output to be 0.5 the period of x1.

    xyce_digital_lib_patgenx2

    Sub-circuit Definition for Xyce Digital PATGENX2

  3. The frequency of the pulse generator is set using PulseFreq = 5e1. Setting the frequency to 5e1 will give us a 20 ms period on the x1 source output.

    qucs_sch_ahah_mr_and2_2pat_pg_sel

    Select PATGENX2 Component

  4. We have set the parameter ScaleFactor = 1 will set the voltage on x1 and x2 outputs to 1 V so both will transition from 0 V to 1 V for their low and high output states.

    qucs_sch_ahah_mr_and2_2pat_pg_params

    PATGENX2 Pulse Parameters

    qucs_sch_ahah_mr_and2_2pat_pg_set

    Xyce PATGENX2 Settings

  5. Click Apply to set the frequency value.

  6. Click OK to exit the properties dialog.

  7. The updated parameters for the X1 Sub-circuit are displayed for the PATGENX2 component.

    qucs_sch_ahah_mr_and2_2pat_pg

    Xyce PATGENX2 Setup

NOTE: Again the parameters for x2 are set to be half of the period of x1. This will give us twice the number of pulses on the input of the memristor MR2 and allow use to generate the truth table for the gate inputs.

  1. Select .Model directive DMOD, from the Xyce Digital Technology library model from the Knowm_Memristor_TTL_Technology library to assign for it to the PATGEN2X pulse generator symbol.
    qucs_lib_xyce_digital_tech_dmod

    Xyce Digital TTL Tech – DMOD Model

    NOTE: The .Model directive for all Xyce Digital components use the model DMOD which is of type DIG as defined in the digital library model source.

    qucs_sch_ahah_mr_and2_2pat_pg_model

    Xyce PATGENX2 Model Parameters

Configure the Transient Simulation in the XYCE Script

  1. The XYCE script component symbol has been added to the schematic to define the transient analysis and variables to be output by the Xyce .PRINT statement.

    qucs_sch_ahah_mr_and2_2pat_xyce_scr

    Xyce Script

  2. The .TRAN start and end time have been set to 1n and 20 ms repectively.

    qucs_sch_ahah_mr_and2_2pat_xyce_scr_set

    Xyce Script Settings

  3. Notice that we have also introduced a new powerful feature of the Xyce script .MEASURE. This provides a means of calculating a analytical quantity during each time step of the transient simulation. Here we have defined the equation EQN {V(W1)*I(VPR1)} and EQN {V(W2)*I(VPR2)}which will compute the power PMR1 and PMR2 through each memristor during the simulation and put result in an output array that can be plotted or used in post-analysis routines.

  4. Click Apply to save the changes.

  5. Click OK to exit the properties dialog.

    qucs_sch_ahah_mr_and2_2pat_xyce_scr_meas

    Xyce .MEASURE Directive

Save the Schematic Diagram File

  1. Click the Save button on the toolbar to save changes to the ahah_mr_AND2.sch schematic file.
    qucs_toolbar_save

    Save Toolbar Button

Run a Simulation

  1. Press F2 or select Simulate button on the toolbar.

    qucs_toolbar_run

    Run Simulation Toolbar Button

  2. Check simulation for errors or warnings. See the status bar at the bottom of the Qucs window lower right corner.

  3. Click the Exit button to close the Simulation window.

View the Tabular Results

  1. Check the Tabular results.

    qucs_sch_ahah_mr_and2_2pat_tab

    Tabular Results

Timing Diagram of Memristor-based AND2 Gate ( V vs. Time ) Results

  1. You can display the timing results in the specified Timing Diagram placed from the diagrams in the Components tab of the Main Dock.

    qucs_sch_ahah_mr_and2_2pat_vt_diag

    Timing Diagram

Cartesian Plot of Memristor-based AND2 Gate ( V vs. Time ) Results

  1. You should also observe the results in the specified Cartesian plot defined in the schematic.

    qucs_sch_ahah_mr_and2_2pat_plot

    Voltage Input, Output with Memristor Power vs. Time

    NOTE: The results contain multiple pulses of the 1V amplitudes for w1 and w2 we defined in the PATGENX2 settings. This plot not only provides the 4 states of the AND gate as shown before but we have also plotted the calculated power PMR1 and PRM2 vs V(OUT) and provided those quantites on the Y2 axis of the plot.

Open the AHaH 1-2 Synapse AND2 Schematic diagram

  1. Double click the AHaH_Logic_prj to automatically open the Content tab.

  2. Select the ahah1-2_synapse_AND2.sch from Schematics in the Contents tab of the Main Dock.

    qucs_sch_ahah_1-2_synapse_and2_2pat_comp

    AHaH 1-2 Synapse AND2 Circuit

  3. We have selected the AHaH1-2 symbol from the Knowm_AHaH library and placed it on the schematic.

    qucs_lib_ahah_tech_1-2_synapse_sel

    Select AHaH1-2 from Knowm_AHaH Lib

  4. The sub-circuit X2 defines the sub-circuit provided for the AHaH1-2 synapse and replaces the two discrete memristors MR1 and MR2 from the last exercise.

    qucs_sch_ahah_1-2_synapse_and2_2pat_set

    AHaH 2-1 Synapse

    NOTE: Again we are using is the AHaH 1-2 synapse AND configuration from the diagram above and the .Model directive MRM5, the M-MSS model from the Knowm_Memristor_Technology library has been assigned for both the X2 sub-circuit memristor symbols.

  5. The parameters for the AHaH1-2 component are already set so no further setup is necessary other than specifying the Rinit parameter using the .PARAM component from the SPICE specfic sections drop-down list in the Components tab of the Main Dock.

    knowm_ahah_lib_ahah1-2

    Knowm_AHaH Lib

Save the Schematic Diagram File

  1. Click the Save button on the toolbar to save changes to the ahah1-2_synapse_AND2.sch schematic file.
    qucs_toolbar_save

    Save Toolbar Button

Run a Simulation

  1. Press F2 or select Simulate button on the toolbar.
    qucs_toolbar_run

    Run Simulation Toolbar Button

  2. Check simulation for errors or warnings. See the status bar at the bottom of the Qucs window lower right corner.

  3. Click the Exit button to close the Simulation window.

View the Tabular Results

  1. Check the Tabular results.

    qucs_sch_ahah_1-2_synapse_and2_2pat_tab

    Tabular Results

Cartesian Plot of Memristor-based AND2 Gate ( V vs. Time ) Results

  1. You should also observe the results in the specified Cartesian plot defined in the schematic.

    qucs_sch_ahah_1-2_synapse_and2_2pat_plot

    Voltage Inputs with Power, Output vs. Time

    NOTE: Again the results are the same as shown before using the discrete memristors and contain multiple pulses of the 1V amplitudes for w1 and w2 we defined in the PATGENX2 settings. This plot not only provides the 4 states of the AND gate as shown before but we have also plotted the calculated power PMR1, PRM2 vs V(W1), V(W2) respectively.

Open the AHaH 1-2i Synapse OR2 Schematic diagram

  1. Double click the AHaH_Logic_prj to automatically open the Content tab.

  2. Select the ahah_1-2i_synapse_OR2.sch from the Schematics list in the Contents tab of the Main Dock.

    qucs_sch_ahah_1-2i_synapse_or2_2pat_comp

    AHaH 1-2i Logic OR2 Circuit

  3. For this example we are using is the AHaH 1-2i (inverted) synapse OR configuration from the diagram above and the .Model directive MRM5, the M-MSS model from the Knowm_Memristor_Technology library has been assigned for both the MR1 and MR2 memristor symbols.

    qucs_sch_ahah_1-2i_synapse_or2_2pat_set

    AHaH 1-2i Synapse

Observe the 2-Pattern Pulse Gererator Voltage Source

  1. The PATGENX2 was introduced in the previous AND2 schematic to replace the 2 rectangle pulse sources in the schematic. Again, for the OR2 schematic this is a component found in the Xyce Digital library components list.

    qucs_sch_ahah_1-2i_synapse_or2_2pat_model

    Xyce PATGENX2 Model and AHaH 1-2i Synapse

  2. Again the PG symbol on the schematic is associated with sub-circuit X1 and the parameters have been set for the PATGENX2 pulse generator source.

  3. The frequency of the pulse generator is set using PulseFreq = 5e1. Setting the frequency to 5e1 will give us a 20 ms period on the x1 source output.

  4. We have set the parameter ScaleFactor = 1 will set the voltage on x1 and x2 outputs to 1 V so both will transition from 0 V to 1 V for their low and high output states.

    NOTE: The definition of the component specifies the x2 source output to be 0.5 the period of x1.
    Again the parameters for x2 are set to be half of the period of x1. This will give us twice the
    number of pulses on the input of the memristor MR2 and allow use to generate the truth table for
    the gate inputs.

  5. The .Model directive DMOD, has been selected from the Xyce Digital Technology library model to assign for it to the PATGEN2X pulse generator symbol.

    NOTE: The .Model directive for all Xyce Digital components use the model DMOD which is of type DIG as defined in the digital library model source.

Transient Simulation Configuration in the XYCE Script

  1. The XYCE script component symbol has been added to the schematic to define the transient analysis and variables to be output by the Xyce .PRINT statement.

    qucs_sch_ahah_1-2i_synapse_or2_2pat_xyce_src

    Xyce Script for Transient Simulation

  2. The .TRAN start and end time have been set to 1n and 20 ms repectively.

  3. Notice that we have again included the .MEASURE lines. This provides a means of calculating a analytical quantity during each time step of the transient simulation. Here we have defined the equation EQN {V(W1)*I(VPR1)} and EQN {V(W2)*I(VPR2)}which will compute the power PMR1 and PMR2 through each memristor during the simulation and put result in an output array that can be plotted or used in post-analysis routines.

Save the Schematic Diagram File

  1. Click the Save button on the toolbar to save changes to the ahah_1-2i_synapse_OR2.sch schematic file.
    qucs_toolbar_save

    Save Toolbar Button

Run a Simulation

  1. Press F2 or select Simulate button on the toolbar.
    qucs_toolbar_run

    Run Simulation Toolbar Button

  2. Check simulation for errors or warnings. See the status bar at the bottom of the Qucs window lower right corner.

  3. Click the Exit button to close the Simulation window.

View the Tabular Results

  1. Check the Tabular results.

    qucs_sch_ahah_1-2i_synapse_or2_2pat_table

    Tabular Results

AHaH 1-2i OR2 Gate Cartesian Plot ( V vs. Time ) Results

  1. Observe the results in the specified Cartesian plot defined in the schematic.

    ucs_sch_ahah_1-2i_synapse_or2_2pat_vt_cart_plot

    Voltage Inputs, Output vs. Time

    NOTE: The results contain multiple pulses of the 1V amplitudes for w1 and w2 we defined in the PATGENX2 settings. This plot not only provides the 4 states of the AND gate as shown before but we have also plotted the calculated power PMR1 and PRM2 vs V(OUT) and provided those quantites on the Y2 axis of the plot.

    or_truth_table

    OR Gate Truth Table

  2. In the first 5 ms both p1 and p2 are positive 1 V so the out state is also positive 1 V or logic 1.

    qucs_sch_ahah_1-2i_synapse_or2_2pat_vt_cart_plot_s1

    First Logic State ( 0 – 5ms )

  3. In the next 5 ms both p1 is positive 1 V but p2 is 0V so the out state is 1 V or logic 1.

    qucs_sch_ahah_1-2i_synapse_or2_2pat_vt_cart_plot_s2

    Second Logic State ( 5ms – 10ms )

  4. In the next 5 ms both p1 is 0 V but p2 is 1 V so the out state is still 1 V or logic 1.

    qucs_sch_ahah_1-2i_synapse_or2_2pat_vt_cart_plot_s3

    Third Logic State ( 10ms – 15ms )

  5. In the last 5 ms both p1 and p2 are positive 0 V so the out state is also positive 0 V or logic 0.

    qucs_sch_ahah_1-2i_synapse_or2_2pat_vt_cart_plot_s4

    Fourth Logic State ( 15ms – 20ms )

That completes this tutorial. Try some of the other example schematic files available in the AHaH_Logic_prj project. All of these experiments use common features presented here. In our next tutorial we will explore more circuits using AHaH nodes that we’ve presented here to simulate machine learning methods.

You should also checkout the documentation and other examples listed in the Qucs 0.0.19 and Qucs-S 0.0.19 documentation available on the web at the following URLs.

Other References

Further Resources

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Michael Arendall

Michael Arendall

Michael Arendall is an experienced software developer, entrepreneur and innovator with more than 25 years experience working with leading semiconductor manufacturers, academia and government laboratories; directly supporting research and development labs by building tools and apparatus for characterizing, analyzing and performing reliability studies on advanced semiconductor process nodes.

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