Intro to neuroinformatics 🧠

    Neuromorphic Circuits

    Neuromporphic circuits make use of analog subthreshold electronic circuits. The perfect emulation of the biophysics of proteic channels.

    Why transistors?

    By varying the gate voltage we are able to control the amount of current flowing through the transistor (in an exponential manner).
    200
    The transistor can operate in two regimes. Subthreshold and above threshold.
    400
    Here we can see that the curve is similar to an IV curve from a channel.
    400

    N-FETs

    Subthreshold

    300
    Where the bulk, $V_{b}$ is connected to $GND$. The current flows from drain to source (think about electron source) and depends on:

    $I_{ds} = I_{0}e^{\kappa V_{g}/U_{T}}(e^{-V_{s}/U_{T}}-e^{-V_{d}/U_{T}})$
    which is equivalent to:

    $I_{ds} = I_{0}e^{\kappa V_{g}/U_{T}-V_{s}/U_{T}}-I_{0}e^{\kappa V_{d}/U_{T}-V_{s}/U_{T}}= I_{f}-I_{r}$

    If $V_{ds} > 4 U_{T}$ the $I_{R}$ term becomes negligible and we operate in the saturation regime and the equation simplifies to

    $I_{ds} = I_{0}e^{\kappa V_{g}/U_{T}-V_{s}/U_{T}}$

    Variables

    • $I_{0}$ current-scaling parameter.
    • κ subthreshold slope factor $\kappa = \frac{C_{OX}}{C_{OX}+C_{dep}}$.
    • $U_{T}$ the thermal voltage.
    • $Vg$ the gate voltage,
    • $Vs$ the source voltage,
    • $Vd$ the drain voltage

    In subthreshold, for a constant $I$, a $ΔV$ change in the source voltage means that the gate voltage has to increase by $𝜅ΔV$ and not just $ΔV$.

    Current characterisation

    Given a ready made transistor, we can influence $I$ with $V_{gs}$ and $V_{ds}$
    400
    400

    We can view this in three dimensions to get a better grasp of it.
    400

    P-FETs

    300
    Where the bulk, $V_{b}$ is connected to $V_{dd}$
    400

    Operating regimes

    400

    Subthreshold

    Linear or ohmic or triode

    Saturation

    $V_{ds}>4U_{T}(100mV)$
    350
    As increases beyond , the concentration of electrons at the drain end
    of the channel can be neglected with respect to the concentration at the source
    end because of the larger barrier height as shown in Fig. 3.5(c). Any electrons
    in the channel that diffuse close to the drain are immediately swept into the
    drain by the electric field in this region. Because the diffusion current is no
    longer dependent on the electron concentration at the drain, the current in
    the transistor depends only on and is approximately equal to.

    This region of operation is called the saturation region. As seen in Fig. 3.7, the
    current is approximately constant in this region. Figure 3.8 shows a family
    of curves measured from the same nFET in the subthreshold region with gate
    voltages ranging from $0.3 V$ to $0.7 V$.

    In these curves, the transition point fromthe linear region to the saturation region occurs around $V_{ds}=100 mV$ and is independent of the gate voltage.

    Superthreshold

    Pasted image 20230125115340.png
    The equations change a bit, but luckily we dont work much in this regime

    Saturation

    Triode

    The circuits

    Change my mind!