Overview

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Who

Carsten Wulff

Why

Example of a temperature sensor

How

One way to make a temperature sensor is to create a temperature dependent oscillator, and then measure the frequency of the oscillator. In Figure 0 we can see an overview.

A bandgap circuit is used to make a current that is proportional to absolute temperature ($I_{PTAT}$) and a voltage that is complementary to absolute temperature ($V_{CTAT}$). A relaxation oscillator converts the current and voltage into a frequency ($f_{OSC}$). A digital finite-state-machine and a counter converts the frequency to a digital value that is proportional to temperature.

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_{Figure 0: System overview}

This temperature sensor was made to conform to the specification at The Project: Design a temperature sensor.

For more information on the oscillator, see Schematics.

To measure the frequency of the oscillator we need a frequency reference. One reference that is usually available in a MCU system is a 32768 Hz oscillator ($f_{32KI}$ in Figure 0). The reason for that specific frequency is to accurately be able to count to 1 second with a binary counter, and apparently to have a frequency for the crystal that is higher than 20 kHz, so we can’t hear it (according to https://youtu.be/_2By2ane2I4?si=8ltUNqAPL71zCQUW).

The principle of operation of the FSM and counter can be seen in Figure 1.

The FSM starts in a IDLE state where a counter is reset. Next the temperature dependent oscillator is started, and a number of oscillator pulses are counted. The FSM runs on LF_CLK and we use the count x LF_CLK to measure the oscillation frequency.

After one clock period the FSM powers down the oscillator. In the CAPTURE state the value of the counter is stored, and the FSM returns to idle.

[Image: SVG not converted]

_{Figure 1: Finite-State Machine to control temperature sensor}

A waveform of the sequence can be seen in Figure 2. When the signal start is asserted the FSM transitions to power up the oscillator (pwrupOsc=1), and we can notice the clkOsc counts the clock pulses of the oscillator. On the next lfClk the oscillator is shut down and the counter naturally stops. The value from the oscillator is stored in the cycles register.

Image: remote

_{Figure 2: Waves from simulation of the oscillator}

In the testbench I store the cycles, and the testbench temperature to a file, and use tb.py to plot the transfer function.

I use a physical model of the oscillator (LELO_TEMP.py) to create a function to turn the frequency back to a temperature. It can be seen that the frequency has a non-zero second order derivative, and thus, the shape of the curve needs to be compensated for. See the python model for details.

Image: remote

_{Figure 3: Simulation of the verilog model of the oscillator}

What

What	Cell/Name
Schematic	design/LELO_TEMP_SKY130A/LELO_TEMP.sch
Layout	design/LELO_TEMP_SKY130A/LELO_TEMP.mag
Verilog Model	design/LELO_TEMP_SKY130A/LELO_TEMP.v
Verilog Counter	rtl/tempCounter.v
Verilog Fsm	rtl/tempFsm.v
Verilog TB	sim/tb_lelo_temp/tb.v
Analog top TB	sim/LELO_TEMP/tran.spi

Signal interface

Signal	Direction	Domain	Description
VDD_1V8	Input	VDD_1V8	Main supply
PWRUP_1V8	Input	VDD_1V8	Power up the temperature dependent oscillator
OSC_TEMP_1V8	Output	VDD_1V8	Temperature dependent frequency
VSS	Input	Ground

Key parameters

Parameter	Min	Typ	Max	Unit
Technology		Skywater 130 nm
AVDD	1.7	1.8	1.9	V
Oscillation frequency	1.7	3.0	4.0	MHz
Temperature	-40	27	125	C

Simulation graphs

Typical temperature error of the sensor is low, but I’ve calibrated the second order correction for typical conditions.

Over mismatch and extreme test condition (ETC) the temperature error increase.

Image: remote

_{Figure 4: Typical simulation results of the oscillator}

Image: remote

_{Figure 5: Mismatch simulation of the oscillator}

Image: remote

_{Figure 6: Extreme test conditions (PVT) simulation of oscillator}

Install

Clone LELO_TEMP_SKY130A

To install, do the following

python3 -m pip install cicconf
git clone --recursive https://github.com/wulffern/lelo_temp_sky130a lelo_temp_sky130a
cicconf --rundir ./ --config lelo_temp_sky130a/config.yaml clone --https

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.

[Image: SVG not converted]

LELOTEMP_OTAN

[Image: SVG not converted]

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

[Image: SVG not converted]

LELOTEMP_CCMP

[Image: SVG not converted]

LELOTEMP_CMP

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

[Image: SVG not converted]

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.

[Image: SVG not converted]

Simulations

LELO_TEMP_SKY130A

LELOTEMP_BIAS_IBP

README.md: “f663125 Sun Mar 8 15:51:30 2026 +0100 “

Loop stability (lstb)

Check stability

Name	Parameter		Min	Typ	Max	Unit
Gain Margin	gm_db	Spec	-50.00	-10.00	-10.00	dB
		Sch_typ		-16.06
		Sch_etc	-19.61	-16.09	-12.33
		Sch_3std	-18.73	-15.78	-12.83
DC gain	lf_gain	Spec	50.00	40.00	80.00	dB
		Sch_typ		69.02
		Sch_etc	66.27	67.43	70.29
		Sch_3std	66.46	68.89	71.31
Phase Margin	pm_deg	Spec	45.00	60.00	90.00
		Sch_typ		60.84
		Sch_etc	46.37	61.01	71.78
		Sch_3std	51.32	60.05	68.78
Unity Gain Frequency	ug	Spec	3.00	15.00	100.00	MHz
		Sch_typ		5.79
		Sch_etc	2.57	5.26	9.50
		Sch_3std	3.62	5.66	7.71
PMOS gate	v(lpo)	Spec	0.45	0.70	1.10	V
		Sch_typ		0.76
		Sch_etc	0.52	0.78	1.05
		Sch_3std	0.73	0.76	0.78
Delta diode voltage	vd	Spec	80.00	106.00	150.00	mV
		Sch_typ		109.24
		Sch_etc	84.63	115.00	145.74
		Sch_3std	104.79	108.96	113.13
Output current	i(v1)	Spec	0.50	1.00	2.00	uA
		Sch_typ		1.09
		Sch_etc	0.81	1.13	1.75
		Sch_3std	0.63	1.15	1.67
VD Error	vdiff	Spec	-6.00	0.00	6.00	mV
		Sch_typ		-0.08
		Sch_etc	-0.32	-0.10	0.06
		Sch_3std	-22.99	0.96	24.91

Transient (tran)

Check settling time and current variation

Parameter		Min	Typ	Max	Unit
t_settle	Spec	0.01	0.05	2.00	us
	Sch_typ		0.32
	Sch_etc	0.28	0.35	0.58
	Sch_3std	0.29	0.32	0.34
i0	Spec	0.500	1.000	2.000	uA
	Sch_typ		1.160
	Sch_etc	0.813	1.169	1.667
	Sch_3std	0.698	1.131	1.564
i1	Spec	0.500	1.000	2.000	uA
	Sch_typ		1.160
	Sch_etc	0.812	1.169	1.666
	Sch_3std	0.705	1.123	1.541
i2	Spec	0.500	1.000	2.000	uA
	Sch_typ		1.159
	Sch_etc	0.812	1.168	1.666
	Sch_3std	0.699	1.114	1.528
i3	Spec	0.500	1.000	2.000	uA
	Sch_typ		1.159
	Sch_etc	0.812	1.167	1.665
	Sch_3std	0.731	1.115	1.499
idd	Spec	5.000	30.000	60.000	uA
	Sch_typ		41.990
	Sch_etc	32.794	40.880	51.902
	Sch_3std	33.968	41.259	48.550

DC (dc)

Check temperature performance

Parameter		Min	Typ	Max	Unit
ibp_err_max	Spec	-30.00	0.00	20.00	nA
	Sch_typ		8.36
	Sch_etc	7.45	8.37	9.54
	Sch_3std	4.00	8.23	12.47
ibp_err_min	Spec	-30.00	0.00	20.00	nA
	Sch_typ		-18.42
	Sch_etc	-21.04	-18.43	-16.39
	Sch_3std	-28.36	-17.72	-7.09
imax	Spec	0.50	0.00	2.00	uA
	Sch_typ		1.46
	Sch_etc	1.29	1.46	1.67
	Sch_3std	1.02	1.43	1.85
imin	Spec	0.50	0.00	2.00	uA
	Sch_typ		0.92
	Sch_etc	0.81	0.92	1.05
	Sch_3std	0.52	0.90	1.28
a_per_c	Spec	1.00	3.00	5.00	nA
	Sch_typ		3.27
	Sch_etc	2.90	3.27	3.75
	Sch_3std	2.75	3.24	3.73

LELOTEMP_OTAN

LELO_TEMP

README.md: “f663125 Sun Mar 8 15:51:30 2026 +0100 “

LELO_TEMP

Temperature sensor (tran)

Check temperature accuracy

Parameter	Description		Min	Typ	Max	Unit
idd_25		Spec	5.000	30.000	100.000	uA
		Sch_typ		79.149
		Sch_etc	57.403	78.516	102.963
		Sch_3std	71.046	80.452	89.858
iddq_25		Spec	0.000	10.000	50.000	nA
		Sch_typ		4.081
		Sch_etc	3.485	4.132	43.674
		Sch_3std	3.785	4.073	4.362
ind_1p_max	Industrial 1 point calibration	Spec	-15.000	0.000	15.000	C
		Sch_typ		9.621
		Sch_etc	2.106	7.344	17.392
		Sch_3std	-6.021	7.607	21.234
ind_1p_min	Industrial 1 point calibration	Spec	-15.000	0.000	15.000	C
		Sch_typ		-5.879
		Sch_etc	-68.311	-7.991	-0.211
		Sch_3std	-12.205	-6.163	-0.121
ind_2p_max	Industrial 2 point calibration	Spec	-10.000	0.000	10.000	C
		Sch_typ		1.855
		Sch_etc	0.188	3.194	11.551
		Sch_3std	-1.705	1.190	4.084
ind_2p_min	Industrial 2 point calibration	Spec	-10.000	0.000	10.000	C
		Sch_typ		-0.857
		Sch_etc	-57.977	-3.249	1.076
		Sch_3std	-6.913	-2.182	2.549
com_1p_max	Commercial 1 point calibration	Spec	-10.000	0.000	10.000	C
		Sch_typ		2.829
		Sch_etc	-0.735	4.276	9.983
		Sch_3std	-1.903	2.703	7.310
com_1p_min	Commercial 1 point calibration	Spec	-10.000	0.000	10.000	C
		Sch_typ		-2.546
		Sch_etc	-10.324	-2.640	0.067
		Sch_3std	-4.683	-2.156	0.370
com_2p_max	Commercial 2 point calibration	Spec	-5.000	0.000	5.000	C
		Sch_typ		0.014
		Sch_etc	-0.106	1.208	4.367
		Sch_3std	-0.311	0.330	0.970
com_2p_min	Commercial 2 point calibration	Spec	-5.000	0.000	5.000	C
		Sch_typ		-0.710
		Sch_etc	-7.586	-0.859	1.076
		Sch_3std	-2.436	-0.898	0.639
freq_min	Frequency	Spec	1.500	3.000	4.800	MHz
		Sch_typ		1.827
		Sch_etc	1.127	1.832	2.491
		Sch_3std	1.327	1.929	2.530
freq_max	Frequency	Spec	1.500	3.000	4.800	MHz
		Sch_typ		1.827
		Sch_etc	1.127	1.832	2.491
		Sch_3std	1.327	1.929	2.530