In the model developed, the phenomena are treated differently depending on their frequency range. On the contrary, high frequency phenomena, essentially the modulated feedback voltage, are not treated as signals but as data, meaning that no events at those high frequencies are generated.
The model only takes into account the effective feedback power generated by this high frequency modulated signal, which in case of PWM modulation is proportional to the duty cycle [7]. The effective feedback power applied to the sensing resistor varies in the low frequency range related to the thermal phenomena system bandwidth in Fig. This modeling enables drastic simulation time reduction. This sampling period is chosen as a tenth of the closed-loop time constant.
Consequently, it allows a one-thousand reduction of the simulation time compared to a simulation that would take into account the high frequency feedback signal. Frequency domains. Those elements are schematically presented in the figure Fig.
The testbench also includes the optical power stimuli, the stimuli process and some analysis tools. The model of the bolometer corresponds to the VHDL transcription of the discretization of the transfer function 2. This structure would enable to take into account the electrothermal feedback phenomenon [9] of the bolometer itself if needed in the simulation. At the present time, this phenomenon is taken into account through the use of the effective thermal conductance Geff rather than the physical thermal conduction Gth.
The model of the amplifier block only consists in a gain since the bolometer voltage output signal is in the bandpass of the filter located before the amplifier. The model of the controller implements the equations of a digital proportional integral PI controller. The controller block also sets the thermal operating point either in open or closed-loop mode with the VPbias input. The model of the feedback shaping block consists in a gain and saturations corresponding to the PWM modulation.
As mentioned earlier, the high frequency carrier that translates the feedback bandwidth is not taken into account. Only the feedback duty cycle is considered. The optical source generates stimuli with parameterized frequency, amplitude and shape. The analyze blocks simulate instrument tools that monitor and extract properties of the temporal signals such as pick-to-pick values.
Such blocks are used for the determination of the transfer functions. Block diagram of the complete testbench. The filled box with dotted border represents the smart-bolometer to be integrated, i.
All the boxes correspond to standard VHDL files. Sclock is the sampling signal at frequency fS. Examples of simulation results This section illustrates the type of simulations that can be done with this modeling technique. The simulations were performed using ModelSim Altera 6. Parameters for the sensor and the electronics were taken from [7] and correspond to a macro-scale device so as to enable comparison between simulation and experiments. The simulation parameters explain the large time constant and large time scale used in the simulations.
Performance of integrated bolometers in terms of time constant would be qualitatively the same and quantitatively scaled down by a factor one-thousand approximately; typically 10 ms time constant for integrated bolometer compared to 10 s for the macroscale bolometer considered here.
Each simulation graph is accompanied by a schematic illustrating the configuration of the testbench, especially highlighting the input and output.
Simulation of the bolometer The Fig. The results are in good agreement with experimental results previously obtained [7]. In open-loop simulation Fig. When the optical stimulus is ON Popt high the bolometer heats up and therefore Tbolometer rises, whereas when the optical stimulus is OFF Popt low the bolometer cools down and Tbolometer decreases. On the contrary, during closed-loop simulation Fig.
When the optical stimulus is ON, the feedback power is low, whereas when the optical stimulus is OFF, the feedback power is high. The total amount of power, optical power added to Joule power, is kept constant.
The simulation begins in open-loop configuration a. The square applied optical stimuli Popt induces temperature changes in the bolometer Tbolometer which is the open- loop ouput.
In closed-loop mode configuration b , the temperature is regulated as the feedback power Pfb compensates the incoming optical power. The closed-loop operation of the bolometer enables a direct power reading of the incoming power through the variations of Pfb. The simulations in either open or closed-loop are performed without convergence issues within a few seconds.
This enables fast parameter optimization for the control through series of simulations. The PI controller is calculated so as to speed-up the closed-loop response 10 times and to guaranty adequate stability margins. The time response reduction is clearly visible through the shapes of the outputs in each case, triangular shape for Tbolometer in open-loop and square shape of Pfb in closed-loop.
Simulation of smart-functions The smart functions of the smart bolometer simulated here are of two kinds: diagnostic functions and correction functions. Among the diagnostic functions, the first one is self-test. The self-test feature allows the verification of the thermal and electrical integrity of the bolometer at any time during its operating life.
It provides the user with a qualitative result that informs whether the bolometer is working or not. The second diagnostic function is self-identification. The self-identification feature is a bit more complex than self-test. The self-identification allows the characterization of the sensor and its associated electrical circuitry.
This feature can be used at any time for monitoring the aging of the device and deciding if a calibration is required. This feature is useful, if closed-loop mode operation of the bolometer is considered, in order to extract the forward path parameters bolometer and its conditioning electronics for the evaluation of the parameters of the controller that would drive the feedback path. Among the correction functions, the function simulated in this work is range selection.
This function enables choosing the measurement dynamic of the bolometer operated in closed-loop mode. Moreover, it enables to work around a user-defined operating point. This feature requires the existence of a built-in stimuli input. The signal VPbias , that sets the thermal working point of the system, is used for this built-in stimulation. Typically, self-test is activated by the user with a logic high level on the self-test input pin. When activated, the self-test feature exercises both the entire thermal structure and the electrical circuitry, and in addition in closed-loop mode the feedback path.
The results presented in the Fig. In open-loop mode Fig. Self-test response in open-loop. Pulses on the VPbias input generate Joule heating onto the resistance of the bolometer through the feedback shaping electronics so as to stimulate a response from the device. Presence or absence of pulses at the output, VT, indicates that the device is working properly or not. In closed-loop mode Fig. The different response times in each case illustrate the time constant reduction in closed-loop mode compared to open-loop mode.
Self-test response in closed-loop. Presence or absence of pulses at the output, VPmes, indicates that the device is working properly or not. An adaptative least-mean- square algorithm is implemented using standard VHDL to extract the characteristic parameters of the bolometer while stimuli are applied. This simulation underlines the ability of the modeling technique to validate algorithm supporting smart functions in their operating context using top simulation.
Adaptative algorithms are interesting in that they run in real-time and do not require huge memory means since a few parameters and a few coefficients are stored. The adjustment is performed according to the stimulation input signal and the modeling error between the predicted output of the model and the current output.
This convergence enables the extraction of estimated parameters representing the device, especially the time constant, the DC responsivity and the thermal characteristics of the bolometer. The formulas below describe the adaptative identification algorithm implemented.
Self-identification refers to identification using a built-in stimulus. The same type of identification algorithms can be used for calibration, in that case external optical stimuli are used and identification results are used to derive coefficients stored in a calibration table. Open-loop identification process. A least-mean square adaptative algorithm is implemented for the extraction of parameters in order to identify the bolometer characteristics.
The prediction error corresponds to the difference between this predicted ouput and the open- loop ouput signal VT. According to the error, the estimated parameters are adjusted. The reduction of the error goes with the convergence of the extracted parameters toward their final value. The stimulus is a pseudo random binary sequence PRBS in order to optimize the identification process.
Range selection enables to adapt measurement range of the smart-bolometer to the range of optical signal measured. Open-loop and closed-loop operation modes should be distinguished. In open-loop operation mode, the input range can be modified by changes of the gain of the conditioning electronics or more rarely through the current bias of the sensing resistor of the bolometer.
In closed-loop mode, the input range is selected by the gain of the feedback. The closed- loop mode, in addition, allows input range selection around a user defined operating point. Considering lines or matrices of pixels, the identification smart function associated to closed-loop operation is a way of compensating for the spatial noise caused by the bolometer resistance dispersion due to fabrication process.
Bolometer pixels individually operating in closed-loop mode would be able to compensate for this spatial noise after external calibration or built-in calibration thanks to built-in input stimuli.
In open-loop the measured signal, VT, is a function of the input optical power, responsivity of the bolometer and the gain of the forward path amplifier. Therefore, the transfer function can be adapted to various incoming power ranges by modification of the gain of the amplifier. The modification of the responsivity through the bias current is not relevant because the signal-to-noise ratio is negatively impacted if the responsivity is decreased.
The responsivity has to be as high as possible according to the fabrication technology. An example of transfer function of the bolometer in open-loop is depicted if Fig. The transfer function represents the voltage at the output of the amplifier as a function of the power of the optical stimuli. Saturation occurs here at 10 V because of the amplifier power supply limitation considered for the macroscale simulations.
Transfer function in open-loop of the bolometer and its associated amplification electronics In closed-loop mode, the output signal is a function of the input power and the feedback shaping gain. The overall measurement range is then given by the pulse coded modulation range, the ADC range and the feedback gain.
Therefore the measurement range of the device may be easily modified to measure lower power or higher power optical stimuli by increasing or decreasing the feedback shaping scale factor respectively.
The feedback shaping gain involves the carrier voltage amplitude, the voltage amplitude of the pulse coded modulation and the filtering amplification gain.
The feedback shaping block is the interface block between the electrical domain and the power domain Fig. The feedback shaping gain specifies the voltage change of the output per power unit of applied optical power. A large feedback gain means that small variation at the output of the controller results in large feedback power; the measurement range is then large.
On the contrary, small feedback shaping gain means that large variations at the output of the controller are needed to produce change in the feedback power; the measurement range is the small. The selection of the operating point achievable in closed-loop mode also enables to move the operating point of the transfer function of the bolometer around a user-defined operating point, in order for example, to measure optical power variations in an input optical signal of given mean power value.
These possibilities in closed-loop mode are illustrated in the graph in Fig. Measured output power is represented as percentage of full scale in each case. The full scale is modified through the gain of the feedback block.
Two transfer slopes resulting in two different measurement ranges are shown. A smaller feedback shaping gain in the case of curve 2 compared to the feedback shaping gain of curve 1 leads to a smaller measurement range, i. In addition the transfer curve 3 of Fig. The slope of curve 3 is the same as the one of curve 2 because the same feedback shaping gain is used in both cases. The dynamic output is limited in the cases presented here by the digital controller output considered to be in the [0 V ; 5 V] range.
Such control of the measurement range shall allow the implementation of algorithm that dynamically adjusts the scale to prevent saturation and optimize the resolution.
Transfer functions in closed-loop. The simulation results demonstrate the ability to simulate mixed electrical circuits and multi-physics system using a purely digital environment and an adequate VHDL modeling of all the parts of the system. Various configurations and various algorithms can be validated in their operating context using this modeling technique.
Such fast and robust simulation enables the validation of advanced features for multi- physics systems, here the smart functions of a smart bolometer. The organization of this paper is as follows. In the Quantities can be scalar or composite array and next section we first discuss the most significant records , but must have scalar subelement of a floating features of VHDL-AMS, which are useful in describing point type. In addition to quantities declared explicitly, the functional semiconductor device model.
The some quantities are declared implicitly to represent the advantages of VHDL-AMS in the aspects of multi- dynamic time-varying behavior of a continuous-time technological modeling are also exposed.
In Section 4, the verification of the model of to time. Thermal issues in the integrated circuits are becoming more and more 2. Simultaneous achieved. For this reason, the electrothermal effect is statements can appear anywhere a concurrent signal detailed in Section 5 separately. Finally Section 6 assignment is allowed. Simple Simultaneous statements discusses the results and draws some conclusions.
In the ENTITY part, the peripheral conditions of the system which play an important role in connections are defined via specific nodes related to the solving the set of equations that represent the considered technological domain. Some variables called continuous-time system. In that part, the behavior of a device, break statement is often used as a means of linking the a circuit or a system is described using some equations discrete-event and continuous-time systems.
Table 1 presents a list of technological AMS model of diode. The model interface is described in the and colorimetric domains.
The below mathematical 3. This model has an important common feature: it is a charge-based model, meaning the terminal charges are associated with terminal voltages. EKV 3. This is shown in Fig. The expressions for model equations are given Fig. The results are shown. As can be seen in this section, we have.
D4 4 Verification of Device Models To validate the characteristics of the junction diode we use a full wave rectifier circuit as shown in Fig. To investigate the accuracy of the VHDL-AMS influenced by the temperature distribution inside the models by Hspice, we compare the result of execution semiconductor devices self-heating effects , it is time and error agreement percentage of VHDL-AMS important to simulate the coupled electrical and thermal with Hspice for above-mentioned circuits as shown in systems simultaneously [16, 17].
Because most of the Table 3. Simulation results of these models with both nonlinear semiconductor device models are simulators are comparable and show a good agreement implemented in the circuit simulators, it is advantageous with each other. According to the results, it can be seen to perform electrothermal simulations inside circuit that by increasing the complexity of the circuit, the simulators. The simulation temperature however, must behavioral modeling is the preferred method of be chosen by the user prior to the simulation and hence simulation in a reasonable time and with a reasonable must remain constant at the predetermined value during percentage of error.
In amount of heat and are often operated in high- these circuits which contain millions of transistors in temperature environments; this directly influences both analog and digital blocks on a common substrate, the their static and dynamic operational characteristics, and analog and the digital blocks need to be simulated their associated failure rates.
For these reasons, adding together. Transistor-level simulations are not feasible thermal effects to the circuit simulators requires the use for this purpose. Behavioral modeling offers a possible of thermal circuit networks.
A good approach to way to abstract the features of interest in a circuit block achieving high accuracy is to simulate the coupled in a reasonable time and at a reasonable cost. Since the size of the BEM Boundary Element Method are popularly semiconductor devices is becoming smaller with employed to solve these equations. But using these advanced technology, and since the electrical methods requires large amount of memory space and characteristics of semiconductor devices are greatly long run time of CPU.
In this context, for simplicity, thermal phenomena PLL 55 sec sec 9. In this circuit current represents heat flow and potentials represent Fig. The physical domains. Thus, the thermal interaction is substrate and its boundaries are used: really bidirectional and the self-heating behavior of the device is properly taken into account. Reciprocally, the instantaneous temperature terminal th1, th2 : thermal ; computed by the RC network and back-propagated to end entity rthermal; the thermal node of the n-MOST model is the operating architecture linear of rthermal is temperature of the n-MOST model.
To take into account the thermal effect in this model, the thermal port, tj, is introduced with relative through and across quantities bound to power and temperature respectively. This section variation and case temperature variation versus time presents a few set of results examples.
In the following during commutation of the transistor when the transistor simulations, the values of the thermal network are is stimulated by a square wave stimulus and connected deliberately overstated in order to emphasize the to the thermal RC network.
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