However, according to [ 19 , 20 ], in spite of the fact that there are a variety of amplifier connections used for monitoring photodiodes, most of them are based on the basic current-to-voltage converter CVC connection shown in Fig. In this figure, R f is the negative feedback resistor used to convert the photocurrent into an output voltage linearly related to the light energy.
This optoelectronic circuit is used in both integrated circuits containing a photodiode and a transimpedance amplifier on a single chip, and in discrete designs. According to [ 20 ], the circuit shown in Fig. On the one hand, if the photodiode exhibits very good characteristics and the ambient temperature is held constant at the optimum value, this circuit provides a very high quality output voltage. On the other hand, in the field, outside the laboratory or in applications in which the temperature is not constant, as the responsivity, the shunt resistance, the junction capacitance and the dark current of the photodiode are temperature dependent, and the noise is dependent upon the characteristics of the photodiode and the operating conditions, the uncertainty of measurement of linear photometer circuits based on conventional CVC connections, as the one shown in Fig.
Therefore, photometer circuits based on conventional CVC connections are not robust [ 3 , 4 ].
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From the Control Engineering point of view, in Fig. Therefore, changes in the ambient temperature, uncertainties and noise in the electrical components, noise coming from the power supply, and so on, make the output of the system to deviate considerably from its true value. In [ 19 - 21 ], a robust photometer circuit is presented taking into consideration the fact that in order to improve the disturbance rejection performance of the circuit, the photodiode should be placed in a robust feedback compensation network.
The robust photometer circuit is shown in Fig. The analysis of the relative error between the theoretical sensitivity and the experiemental sensitivity of the circuit shown in Fig.
Also, a detailed analysis of the sensitivity of the photometers shown in Fig. In addition, in [ 22 ] a simplified analysis of the effect of the offset voltage of the op amp on the response of these photometers is presented. Furthermore, in [ 22 ] both the low-frequency noise power estimation analysis and the total harmonic distortion performance analysis of the circuits shown in Fig. Finally, in [ 21 ] a complete analysis of the influence of the op amp parameters on the performance of the circuit in Fig.
However, there is al least one more type of analysis that should be carried out to these circuits. This is the frequency response analysis by using an input-output transfer function approach. This is the aim of the next section. This kind of analysis has the advantage of being directly linked to the time domain, and at each frequency the transfer function has a clear physical interpretation. Also, one important advantage of a frequency response analysis of a system is that it provides insight into the benefits and trade-offs of feedback control.
According to [ 4 ], the most important design objectives which necessitate trade-offs in feedback control are the following:. Performance, good disturbance rejection: loop-transfer function, L s , large. Small magnitude of input signals: controller transfer function, K s , small and L s small. Furthermore, in accordance with the loop-shaping approach to controller design [ 3 , 4 ], a system is robust if the following stability margins are guaranteed: a gain margin GM equal to infinity, a gain reduction margin equal to 0.
Graphically, for a single-input-single-output SISO system, it means that the Nyquist plot of the loop transfer function of the system will always lie outside the unit circle with center -1 in the complex plane see Fig. However, robust stability must not be confused with robust performance [ 3 , 4 ].
A system that is robust could have noise rejection problems. That is to say, measurement noise, high frequency noise and some kind of perturbations can corrupt the relevant information coming from it.
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Nevertheless, a system that has robust performance characteristics has robust stability and has a satisfactory noise rejection performance, among other good properties. According to [ 20 ], assuming that the op amp is ideal see [ 21 ] for the case of the non-ideal op amp , the transfer function of the circuit shown in Fig. And the transfer function of the circuit shown in Fig.
As can be seen from the above equations, 2 is much more complex than 1.
However, 1 cannot deal satisfactorily with disturbances and uncertainties in the parameters of the photodiode, something that is done by 2 satisfactorily [ 20 ]. In addition, in the laboratory experiments the incident light came from the 3 mW RS Modulated Laser Diode Module , whose nominal wavelength is nm, and the experimental sensitivity of the BPW21 at nm was 0. Furthermore, in order to have a 10 V output for a 3 mW input to the circuits shown in Fig.
The loop transfer function of the robust photometer circuit [ 20 ] is. Moreover, the Bode plots of 11 and 12 are shown in Fig. From these figures it can be seen that both closed-loop transfer functions have a similar characteristic at low frequencies, and that the robust circuit has a feedback controller that introduces lead-lag compensations at middle frequencies.
These compensations improve the disturbance rejection performance of the photometer circuit. The Nyquist diagram of the loop transfer function of the robust photometer 13 is shown in Fig. Note that L r s never enters the unit circle, which means that the closed-loop system with the transfer function given by 12 is robust. Also, A , B , C and D are given below. Note the fast, satisfactory convergence of the phase variables i. If the initial condition of the state vector of the system is not zero, the trajectory described by the state variables will converge to one similar to the ones shown in Fig.
Trajectories of the state variables of the system given by 15 - 16 for an input of 3 mW of incident light at 10 Hz, Hz and 1 kHz, respectively. From that figure it can be seen that step disturbances at the output of the plant are rejected satisfactorily. The closed-loop system does not amplify disturbances, its response does not have any oscillatory performance and its response decreases in amplitude very fast.
Response of the robust photometer circuit to a step disturbance at the output of the photodiode. The photometer circuits presented in this paper Fig. Practical implementation of the circuits shown in Fig. Furthermore, in order to test the noise rejection performance of both circuits, a 3 mW incident light input signal at 0 Hz and wavelength equal to nm was apply to the above-mentioned circuits, and the power spectrum of the output voltage of these circuits was displayed by using the YOKOGAWA Digital Oscilloscope DL The result of the experiment was that for the non-robust circuit the peak value of the power spectral density PSD of the noise of the output voltage was equal to However, the peak value of the PSD of the noise of the output voltage was equal to Therefore, a signal-to-noise ratio improvement of 10 dBV was achieved by using the robust compensation.
Moreover, the temperature coefficient TC of the output voltage of the robust photometer circuit was equal to In this paper, an input-output transfer function analysis of a photometer circuit based on an op amp has been carried out. The results of the analysis showed the importance of the application of robust control technique to improve the performance of photometer circuits, and showed some of the most important points to be taken into consideration when designing these circuits for applications in which they have to work under severe working conditions, as it happens in most industrial applications.
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Moreover, here two photometer circuits, one based on a conventional CVC connection and another based on a robust CVC connection, have been compared with each other. The results of such a comparison showed that the performance of photometer circuits based on robust CVC connections is much better that the performance of photometers circuits based on conventional CVC connections.
The use of robust control techniques to the design of complex sensor systems can bridge the gap between advanced signal conditioning techniques and the design of sensors for a wide range of applications. The reality is that only by the fusion of these concepts can the designer find the way clear to build the sensors that today's industry needs. National Center for Biotechnology Information , U. Journal List Sensors Basel v. Sensors Basel. Published online Jan 9. Wilmar Hernandez. Author information Article notes Copyright and License information Disclaimer.
E-mail: se. Received Dec 22; Accepted Jan 7. This article has been cited by other articles in PMC.
Abstract In this paper an input-output transfer function analysis based on the frequency response of a photometer circuit based on operational amplifier op amp is carried out. Keywords: photometer circuit, current-to-voltage converter connection, frequency response, robust control. Introduction Semiconductor junctions convert the photon energy of light into an electrical signal by releasing and accelerating current-conducting carriers within the semiconductor [ 1 ].
The photo effect and photodiode model According to Graeme [ 1 ], light entering a semiconductor material produces an electrical current by releasing hole-electron pairs. The most important characteristics of a photodiode are the following [ 1 , 16 , 17 ]: Spectral response Radiometric sensitivity Responsitivity Quantum efficiency Sensitivity Linearity Dark current Shunt resistance Junction capacitance Reverse breakdown voltage Open circuit voltage Response time Noise current Angular response Package style Also, according to [ 1 , 16 , 17 ], the equivalent circuit for a photodiode is shown in Fig.
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