LELO_TEMP_SKY130A

LELOTEMP_BIAS_IBP

Bandgap core. The voltage across the resistor between VR1 and VD2 will be

\[\Delta V = V_{R1} - V_{D2} = \frac{k T}{q} ln(8 \times 8)\]

since there is a 1-to-8 ratio between the bipolars, and a 1-to-8 ratio in the current mirror.

The current in the resistor will be

\[I_{R} = \frac{\Delta V}{(4 + 8) \times RPPO}\]

Where $RPPO$ is the unit resistor.

The $V_C$ is a bit more complicated, but can be calculated to be

\[V_C = \frac{kT}{q}(\ell - 3 \ln T) + V_G\]

where

\[\ell= \ln{I_D} - \ln{\left (Aq\frac{D_n}{L_n N_A} + \frac{D_p}{L_p N_D}\right)} - 2 \ln{\sqrt{B_c B_v}}\]

where $A$ is the area of the diode, $I_D$ the current in the diode, $D_n,D_p$ are the diffusion constants for electrons and holes. $L_n,L_p$ are the diffusion lengths, $N_A,N_D$ are the acceptor and donor concentration. and $B_c,B_v$ are

\[B_c = 2 \left[\frac{2 \pi k m_n^*}{h^2}\right]^{3/2} \text{ } B_v = 2 \left[\frac{2 \pi k m_p^*}{h^2}\right]^{3/2}\]

where $m_n,m_p$ are the effective mass of electrons and holes and $h$ is Planck’s constant.

Obviously.

Not really.

But it is understandable.

See Diodes

Estimated values from the model in LELO_TEMP.py are shown in table below.

Temperature [C] Current [uA] Vc [V] DeltaV [mV]
-40 0.902 0.8386 83.6
25 1.133 0.7412 106.9
125 1.470 0.5844 142.7

The table was generated from model.ipynb

The diode connected transistor on the right side is to clamp the voltage between VR1 and VD2. If the current is too high, then a high voltage on VR1 can turn off the PMOS in the OTA, and increase settling time.

LELOTEMP_OTAN

LELO_TEMP

Bandgap (LEOTEMP_BIAS_IPB) is used to provide a PTAT current for the frequency conversion and the comparator. The $V_C$ is the CTAT diode voltage in the bandgap. The output current is approximately 1 uA.

The current charges the capacitor inside CCMP. When the voltage on the capacitor reaches $V_C$ the comparator inside CCMP will trigger (low to high).

The two comparators alternate to trigger the set/reset latch made by the NOR gates. As such, the two capacitors are alternatively charged.

The output frequency can be calculated from the voltage/current relationship of a capacitor.

A single charge cycle is given by

\[I = C \frac{dV}{dt} \Rightarrow dt = C \frac{V_C}{I}\]

Inserting for the bandgap current ($I_R$)

\[dt = RC \frac{V_C}{\Delta V}\]

As such, the frequency will be

\[f_{OSC} = \frac{1}{2 dt} = \frac{1}{2RC} \frac{\Delta V}{V_C}\]

The $\Delta V$ increases with temperature and $V_C$ decreases with temperature, turns out the $\Delta V$ increases faster than $V_C$ drops, so the overall gradient is positive.

The estimated frequency is shown in the table below (the table was generated from model.ipynb))

Temperature [C] Frequency [MHz]
-40 1.858
25 2.634
125 4.310

LELOTEMP_CCMP

LELOTEMP_CMP

A two-stage OTA used as comparator. Uses a 1U bias current from the bandgap

TB_LELO_TEMP

A top level debug testbench for the temperature sensor. If you open the testbench in Xschem you’ll see there are waveforms to view signals inside the temperature sensor.

A debug testbench like this is quite useful to figure out what’s going on, and see what voltages and currents are present in the design.