Temperature-to-Digital Converters (TDCs) are on-chip sensors that generate temperature-dependent digital codes.
On-chip temperature measurements have acquired an increasingly important role over the past two decades, especially if we consider sensors that produce data in the digital domain, referred to as Temperature-to-Digital Converters (TDCs). The growing computational power of modern microprocessors has given rise to a higher degree of criticality in their thermal management process 
; for instance, dynamic voltage and frequency scaling (DVFS), a commonly used approach in this framework 
, requires responsive temperature tracking to allow an effective control on the thermal status of the microprocessor and, furthermore, the cooling fans’ speed regulation is also based on a continuous temperature monitoring 
. Another field that has featured a remarkable growth in recent years is the Micro-Electro-Mechanical Systems (MEMS) one 
; the employment of these devices for Internet of Things (IoT) applications, supported by a parallel technological development, has led the research focus to more and more robust devices with respect to the influence of environmental effects. One of the main challenges is, indeed, to mitigate the impact of the ambient temperature on the performance of these devices; the micro-structures used as sensing elements suffer from a significant thermal spread causing a degradation of the reliability of the sensed quantity. For this reason, high-precision MEMS devices also require a temperature tracking to compensate for the drift of their parameters 
. Integrated temperature sensors are also used for clinical applications 
; devices that provide a high accuracy monitoring in the human body temperature range are needed for the detection of atypical biomedical conditions. Lastly, since temperature is a fundamental physical parameter of both industry and everyday life, on-chip temperature measurements are also combined with radio-frequency identification (RFID) tags in several applications: monitoring of the food cold chain 
, environmental monitoring 
, supply chain management of healthcare products 
, animal healthcare monitoring 
and many more.
2. Temperature-to-Digital Converters
There are a lot of applications requiring on-chip temperature sensing, as seen in the introduction, and concern several systems in the microelectronics field; despite their wide range, all the reported examples 
have one important feature in common: they provide temperature information in the form of digital data. This is fundamental as it makes them compatible for a direct communication with digital signal processing (DSP) circuits that can easily handle the needed temperature information and at the same time reduces the complexity of the system they are inserted in; for this reason, they are often referred to as smart temperature sensors 
or as Temperature-to-Digital Converters (TDCs)
. It is important to specify that this category of temperature sensors was born with a cost-minimization perspective and that its development in the past two decades has consequently followed this line; even if, in principle, these fully integrated temperature sensors have significant limitations in terms of accuracy and sensing range with respect to other existing discrete sensors, their great success is related to their compatibility with large-scale production of low-cost products being integrated within the system in which they are operated. Figure 1
shows the conceptual diagram of a TDC.
Figure 1. Conceptual diagram of a Temperature-to-Digital Converter.
It is composed of an Analog Front-End (AFE), an Analog-to-Digital Converter (ADC) and a Digital Back-End (DBE). The TDC’s input signal is temperature; the AFE, the first block of the chain, is responsible to sense it achieving an electrical form for it (either in the voltage or in the current domain) and to generate at its output the signals needed for the Analog-to-Digital conversion: a proportional-to-absolute-temperature (PTAT) signal which contains the information to be converted and a reference (REF) signal, which in principle is a Zero-Temperature-Coefficient (ZTC) signal, with respect to which the conversion is carried out. Those signals enter the ADC which produces PTAT digital words with an intrinsic n-bit resolution and with a data rate (fS) that depends on the converter architecture; this operation is typically performed without the use of sample and hold (S/H) circuits because of the relative slowness of the temperature signal with respect to the common conversion rates of ADCs. The n-bit codes are then processed by the DBE that, in fact, acts as an oversampler; it refines their intrinsic resolution performing decimation and filtering with a certain OverSampling Ratio (OSR) in order to obtain the output codes of the TDC which feature a higher resolution at the cost of a lower data rate (fS/OSR).
The resulting time interval required to perform a single Temperature-to-Digital conversion is therefore given by
Considering the TDC’s minimum working supply voltage (Vsy
) and the current drained from it (Isy
), its conversion energy can be defined as
It is a parameter of paramount importance together with the TDC’s resolution (Res
) which is the minimum temperature difference that can correctly be detected and which is determined by the quantization noise of the ADC, by the electronic noise (thermal, flicker, etc.) and by Tconv
itself. Another parameter of interest is the temperature inaccuracy (IA
); in absolute form, it is a statistical evaluation of the worst case (or ±3σ
) temperature error and, introducing the TDC conversion range (Trange
), its relative form can be expressed as
This quantity is strongly dependent on the number of controlled temperatures at which the TDC gets trimmed (ntrim
, an unavoidable procedure in most applications; the trimming process, which basically consists of calibrating the sensed temperature error, is a cost of great relevance in the TDC framework as heating and cooling the devices to be trimmed is a very time consuming operation. For this reason, ntrim
should be minimized to preserve the cost-effectiveness of the sensor.
Due to the presence of this great variety of parameters of interest, several Figures of Merit (FoMs) have been introduced to provide TDC performance metrics in a synthetic way and from specific perspectives:
(4) and (5), presented in 
, involve the TDC conversion energy together with its resolution or its inaccuracy, respectively. (6), instead, addresses only the production cost of the TDC (Area
is the active silicon area of the device, F
is the feature size of the adopted technological process) while (7) provides a global overview of the TDC performance 
Several ADC architectures have been used, in literature, to be included in TDCs; there are examples of Flash-based TDCs 
, of SAR-based ones 
, of ΣΔ
-based ones 
, of time/frequency-domain-based ones 
or of hybrid solutions 
. It is important to notice that even if, conceptually, Flash ADCs and SAR ADCs are faster for a given quantization noise and clock frequency, to overcome the limits imposed by the presence of thermal noise, their output codes still need to be processed by the DBE and therefore, for the same amount of power consumption, are not automatically at a higher energy efficiency level with respect to the ΣΔ
-based or the time/frequency-domain-based alternatives. Actually, thanks to their versatility, ΣΔ
converters are the most used ones in the case of AFEs generating static temperature-dependent signals while time/frequency-domain-based ADCs are preferred in the case of dynamic temperature-dependent signals.