Passive Channels, Diffusors, and Dendrites

Overview:

Reading:

Project Questions:

One aspect you will want to perform, and might want to include in your video, is a derivation of the diffusor / dendritic line behavior. Passive Channel Transistor Model First, we want to measure a transistor (pFET) as a passive channel, as the prototype for a passive biolgical channel. We will use an FG OTA to input the current into the system; assume the maximum current of the tanh is in fact what is programmed for the device (will be slightly different, but nearly zero impact on your results).

You should have the source as the membrane voltage, the drain at GND, and you should bias the gate at a useful fixed potential for the circuit. The gate voltage will be directly related (and easy to model. Hint for writeup) to the bias current you use for your OTA device. You might find it will help to program your OTA device, and sweep your pFET gate voltage to find a maximum response. You may, and are encouraged to do so, to have a pFET FG.

You will have capacitance from the line which serves fine as the membrane capacitance, From a small-signal step response, estimate the size of your capacitance.

You will want to think about the resulting dynamics in terms of membrane current. We have a dual representation between current and voltage through the pFET device.

In case you are looking for what a plot might look like, Vg at 0.1 V, EK at 1.35V, we have plots, sweeping from 0V to 2.5V where we are explicitly using an ammeter to measure the current. The first plot is for linear scale, and the second plot is log scale, taking the abs( ) of the mesaured current.

Characterizing a Diffusor Line in Routing Fabric

Set all the inputs to zero except the one on one side of the line . Observe the effects of the input level on the output level.

We will Obtain the responses to a subthreshold input current for different values Vr-Vg. These values will be programmed into the FG routing elements.

You will measure the resulting tap voltage (from the diffusor). Remember, we expect that the voltages will decrease linearly with position. Of course, there will be VT0 mismatch due to the indirect programming structure. You will get a very clear picture of how much mismatch we have in these devices. Ideally, the system will have a table of these mismatch values (which is under development to be integrated into the tools). In this case, you will need to figure out the resulting device mismatch.

The good part is one can do this just by injection (fine injection), because one only needs to increment either the set of vertical or horizontal conductances, just slightly shifting the dc point. If one does alot of corrections, you might have to reprogram, only then, but can include the new values.

You need to show at least two linear slopes as a result of two Vr and Vg. Observe how the signal spreads. Plot your results and extract the space constant for both cases. Over how many decades is the response exponential? Is the deviation due boundary effects or offsets? Compare the (at least) two measured space constants versus Vr-Vg with theory.

Next, put in a step input current (step voltage), and look at the resulting dynamics down the line. You should see a delay between stages between 0.03ms to 2ms, which directly affects your input current level (so choose carefully, which means you need to do some analysis). You will likely need to have some amplification to buffer your signals down the line. Capture the waveform dynamics.

Next, put in an input waveform such that the current output would model the output of a synapse, a post-synaptic potential. Capture the waveform dynamics.

Finally, you will want to modify the diffusor line parameters to assist in propagating the input waveform from one end of the line to the other end of the line. This would correspond to having a change in the diameter of the cable, like in a typical dendrite the cable diameter gets larger as one approaches the soma.