Journal of Sensors

Volume 2018, Article ID 3747325, 12 pages

https://doi.org/10.1155/2018/3747325

## A Controllable Constant Power Generator in 0.35 *μ*m CMOS Technology for Thermal-Based Sensor Applications

Correspondence should be addressed to Milena Zogović Erceg; moc.liamg@civogoz.anelim

Received 1 September 2017; Revised 26 November 2017; Accepted 6 December 2017; Published 4 March 2018

Academic Editor: Belén Calvo

Copyright © 2018 Milena Zogović Erceg. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

A CMOS controllable constant power generator based on multiplier/divider circuit is presented. It generates constant power for a wide range of the resistive loads. For the generated power of 5 mW, and the resistance range from 0.5 kΩ to 1.5 kΩ, the relative error of dissipated power is less than 0.6%. For single supply voltage of 5 V, presented controllable constant power generator generates power from 0.5 mW to 7.8 mW, for the load resistance dynamic range from 3 up to 15, while the relative error of generated power is less than 2%. The frequency bandwidth of the proposed design is up to 5 MHz. Through the detailed analysis of the loop gain, it is shown that the circuit has no stability problems.

#### 1. Introduction

The circuit which generates constant power for variable resistive loads finds application in various types of thermal-based sensors, such as mass flow meters, anemometers [1], AC power meters, gas monitoring [2, 3], plant water status monitoring [4], seepage meters [5], and other flowmeters intended for very slow fluids. Thermal-based flow sensors are very attractive because of their simple construction. They basically consist of constant power generator and sensing element. The surrounding fluid transfers heat to/from sensing element depending on its flow rate. As the temperature of the sensing element is changed, its resistance is changed, and the constant power generator changes the voltage drop across the sensing element to keep constant power. Measuring the voltage change across the sensing element, it is possible to extract the information about the fluid flow rate. So, the quality of the constant power generator as a part of the thermal-based sensor is very important. Controllable constant power generator is the circuit which generates constant power dissipation over a range of resistive loads. The control of the generated power is provided by control voltage or control current. The range of resistive loads has to be as large as possible for the particular generated power. In that sense, the quality of constant power generators is determined by the load resistance dynamic range, defined as the ratio of the largest load resistance to the smallest load resistance (*R*_{Lmax}/*R*_{Lmin}), for the particular value of dissipated power. The other important characteristic of the constant power generator is the value of generated power for a given load resistance, depending on specific application. The relative error of generated power over the range of load resistance is the key quality parameter of the constant power generator. Low-supply voltage of constant power generator is critical for many applications as a consequence of the general trend in electronics. The ratio of the largest voltage drop across the resistive load and supply voltage (*V*_{Lmax}/*V*_{DD}) can be used as a quality indicator of constant power generators. One of the main problems in constant power generator design is its stability caused by feedback loops.

There are several designs of constant power generators, developed mostly in BiCMOS and bipolar technologies. A CMOS controllable constant power generator based on the resistive mirror [1] has the range of generated power from 0.48 mW to 10.8 mW, and the load resistance dynamic range up to 28, with the relative error of generated power less than 2.2% and the supply voltage of 10 V. The constant power generator presented in [1] uses four operational amplifiers OP97 which are designed in a complementary bipolar technology, while the rest of the circuit is realized using n-channel MOSFETs. Hence, the circuit [1] can be considered as a BiCMOS technology design. The controllable constant power generator [3], based on CMOS translinear loop, has a load resistance range from 470 Ω to 1.47 kΩ and is able to generate power up to 11 mW, with the supply voltage of ±5 V and the relative error of generated power up to 3%. The circuit presented in [3] uses off-chip operational amplifier LM301 designed in a complementary bipolar technology, while the rest of the circuit is realized in a CMOS technology. Hence, the circuit [3] can be considered as a BiCMOS technology design. Controllable constant power generator [4–6] can change the dissipated power by a factor of 1 : 1000, using the log-antilog circuit with bipolar junction transistors. This controllable constant power generator uses eight OPA4227 operational amplifiers designed in a complementary bipolar technology. Consequently, the circuit [4–6] can be considered as a bipolar technology design. The controllable constant power generator [7] in BiCMOS technology achieves load resistance range of 1 : 50, with generated power up to 100 mW. The microcontroller-based solution [9] can achieve large resistance dynamic range and large power dynamic range, but at the price of reduced frequency bandwidth. The CMOS design proposed in [10] for small variations of the resistive load has a large relative error of the generated power.

Taking into account that the existing designs of controllable constant power generators are designed mostly in BiCMOS and bipolar technologies and that CMOS technology is the most popular and the cheapest technology so far, the goal of this work is the design of fully integrated controllable constant power generator in a pure CMOS technology. This paper presents controllable constant power generator in 0.35 *μ*m CMOS technology based on current-mode multiplier/divider circuit [8]. The generated power can be adjusted by two control currents which are the input currents of the multiplier/divider circuit. Through the detailed analysis and simulations, it is shown that proposed design is able to generate constant power over a large range of the load resistance. The mathematical model for the loop gain of the controllable constant power generator shows that circuit has no stability problems for a wide range of resistance for the particular generated power. The influence of the process parameter variations and the temperature variations to the proposed design is also analyzed.

#### 2. Circuit Description

##### 2.1. Basic Principle

The main purpose of the constant power generator is to maintain the constant power dissipation across the resistive load:
where *P _{L}* is the generated power across the resistive load,

*I*is the current flowing through the resistive load, and

_{L}*V*is the voltage across the resistive load. Generated power has to be independent of the load resistance. Also, it is desirable to have the possibility to control generated power easily.

_{L}The basic principle of the controllable constant power generator with a novel method for achieving a constant power dissipated on the resistive load is shown in Figure 1. It consists of multiplier/divider circuit, second generation current conveyor (CCII), load resistor *R _{L}*, reference resistor

*R*

_{REF}, and two DC current sources

*I*

_{1}and

*I*

_{2}. The output current

*I*of the multiplier/divider circuit is flowing through the resistive load

_{L}*R*. The voltage

_{L}*V*across the resistive load is transferred via CCII to the resistor

_{L}*R*

_{REF}. So, the output current

*I*

_{3}of the CCII is given by