Introduction

The main advantages of traffic lights with LED application are better luminous efficiency and reliability, compared to incandescent-based traffic lights. Traffic flow can be controlled using by traffic lights [1]. For a given location, the traffic lights are able to indicate and provide the information about the ambient. In existing traffic information systems, the signals of traffic light are used to transmit traffic message using by display traffic jam on a map.

Flicker is dependent on operated parameters of LED source, such as spectrum, frequency, bias voltage, amplitude factor, voltage amplitude, and distance [2, 3]. The signal-to-noise ratio (SNR) is a key factor of the signal transmission of smart traffic information system. The signal transimission performance of traffic system is related to a variety of factors such as the SNR, illuminance and frequency [4].

The value of SNR is 15 dBs for minimum acceptable range of traffic information application [5]. However, it is incorrect to assume that the SNR is constant in smart traffic system applications. It should point out that both of the light output of traffic application are sensitive to the operated conditions of LED sources. The light output of LED source with forward voltages and frequency were compared to evaluate the effects of the electrical properties on the SNR [6].

Several factors are influence on signal transmission of traffic information system. These factors include heatsink temperature and driver parameters, which is not considered into the system modeling. SNR is a key parameter of smart traffic information applications; however, it has not been any substantial investigate on the operated effects of traffic light with sinusoidal waveform driver on illuminance and SNR. Flicker for traffic lights is highly dependent on the driver operation.

A periodic waveform is dependent on seveal parameters, such as voltage amplitude, duty cycle, frequency etc. Therefore, the properties of a sinusoidal waveform can be determined as bias voltage, amplitude voltage, frequency and amplification factors. The properties of a sinuoidal waveform influences on human eye response. If frequencies is higher than 70 Hz, obvious detection of light flicker can cause uncomfortable symptoms of human beings [7]. Flicker also can be observed in signal transmission when the traffic light interacts with moving objects.

It is important mentioned that many light sources inside smart traffic information system display obvious flicker. Reduction flicker of light sources inside traffic information system is using by electronic solutions, which is major cause of lower power efficiency [8]. Reduction flicker of light source can also acquire using by slow-decay phosphors [9]. The optical variation performance of LED source with sinusoidal waveform driver in smart traffic information system is not well understood. In practice, the electronic engineer or the signal designers are not familiar with optical controll for LED application with luminous efficiency, color characteristics, and reliability design.

The practical performance of the mixed light output of the mixed white LED source with a warm white LED and a cool white LED under sinusoidal waveform driver is investigated. The proposed model includes the variations on the heatsink temperature, bias voltage, amplitude voltage, frequency and amplification factors. The proposed model can estimate the illuminance and SNR with different heatsink temperature and driver parameters that cannot be easily evaluated in practice. The proposed model cover extends the illuminance and SNR of LED source inside smart traffic information system to include the key parameters of sinusoidal waveform. It is pointed out that the proposed model can be used as a design tool for traffic designs. The work is important to signal transmission of smart traffic information system designers because the operating temperature and driver parameters of LED sources may change.

Methods

Smart traffic information system transmits information from light source to detector. The most important ability of smart traffic information system is to detect signals including given information with background noise [10, 11]. Traffic light can be used for signal transmission based on vehicle infrastructure system. The network of smart traffic information includes left turn assistant, lane change warning, and pre-cash sensing [3, 12, 13], as shown in Fig. 1.

Fig. 1
figure 1

Network of smart traffic information system

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The SNR is related to the acquired light power, which means that smart traffic information system perform high signal transmission mass with low signal loss. The noise sources of smart traffic information system are critical factors of signal distortion performance.

The LED should be used as signal transmission and lighting application. The illuminance, heatsink temperature and driver parameters of LED systems are highly related to each other. Modelling of the photometric, electric, thermal and colorimetric aspects of white LED devices is proposed [14]. The photo-electro-thermal (PET) theory has provided a series studying for the white LED system. There are given technical specifications for LED systems based on Energy Star Program and IEC standards [15, 16]. The proposed new PC-LED model considered several factors, such as energy-storage and dynamic properties of the phosphor coating. This new model can accurately predict dynamic optical and energy loss in PC LED device [17, 18].

Normally, the illuminance is dependent on the heatsink temperature, voltage amplitude, and bias voltage. The relationship is reflected on the heatsink temperature and illuminance of LED with the constant voltage amplitude and bias voltage as shown in Fig. 2. LED sample is mounted on a temperature-controllable heatsink. The illuminance as a function of the heatsink temperature for constant LED voltage amplitude and bias voltage operation is fairly linear. Therefore, the illuminance of LED as a function of the heatsink temperature Ths for constant LED voltage amplitude Va,0 and bias voltage Vb,0 operation can be approximated as a linear relationship.

$$E\left({T}_{\mathrm{hs}},{V}_{\mathrm{a},0},{V}_{\mathrm{b},0}\right)={a}_1{T}_{\mathrm{hs}}+{a}_2$$
(1)
Fig. 2
figure 2

Illuminance versus heatsink temperature of LED device under “constant voltage amplitude and constant bias voltage” operation

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Where α1 is a constant representing the slop and α2 is another constant. Both α1 and α2 can be obtained from the measurement in Fig. 2.

Using the Everfine LFA-3000 light flicker analyzer system, the practical measurements of the illuminance as a function of the LED voltage amplitude under “constant heatsink temperature and constant bias voltage” operation are obtained and shown in Fig. 3. Therefore, it is can be given as

$$E\left({V}_a,{T}_{\mathrm{hs},0},{V}_{b,0}\right)={\beta}_1{V_a}^2+{\beta}_2{V}_a+{\beta}_3$$
(2)
Fig. 3
figure 3

Illuminance versus voltage amplitude of LED device under “constant heatsink temperature and constant bias voltage” operation

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Where β1, β2, and β3 are coefficients that can be extracted from Fig 3 with constant heatsink temperature and bias voltage.

Based on the above analysis, E can be obtained as heatsink temperature Ths and voltage amplitude Va with constant bias voltage using a two-dimensional mathematical function. Similar modeling method based on the 2D linear behavior has been proposed to [14]. Therefore, the illuminance E can be constructed as in the following

$$E\left({V}_a,{T}_{\mathrm{hs}},{V}_{b,0}\right)=\frac{E\left({T}_{\mathrm{hs}},{V}_{\mathrm{a},0},{V}_{\mathrm{b},0}\right)E\left({V}_a,{T}_{\mathrm{hs},0},{V}_{b,0}\right)}{c_1}$$
(3)

Where c1 is intersection values of (1) and (2). It should be pointed out that the model can predict the illuminance of the LED at any heatsink temperature and voltage amplitude with constant bias voltage. Equation (3) links the illuminance to heatsink temperature and voltage amplitude together under constant bias voltage operation.

The illuminance of the LED device is highly related to the bias voltage. To establish the dependence on illuminance E on the bias voltage, the LED device is operated in the bias voltage 1 to 5 V under constant heatsink temperature Ths,0 and constant voltage amplitude Va,0 operation. Generally, illuminance E obviously increases with bias voltage, as shown in Fig. 4. The theoretical model of the illuminance behavior as quadratic function of the bias voltage is indicated in Fig. 4, as shown in the following.

$$E\left({V}_b,{A}_{a,0},{T}_{hs,0}\right)={\chi}_1{V_b}^2+{\chi}_2{V}_b+{\chi}_3$$
(4)
Fig. 4
figure 4

Illuminance versus bias voltage of LED device under “constant voltage amplitude and constant heatsink temperature” operation

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Where χ1, χ2, and χ3 are coefficients that can be extracted from the experimental results in Fig. 4.

Combined with (3) and (4), the behavior of the illuminance of the LED is given by 3-D nonlinear function, as shown in (5), where c2 is the intersection value of function of (3) and (4). It is a model that combines the heatsink temperature Ths, amplitude voltage Va and bias voltage Vb aspects of an LED source.

$$E\left({V}_a,{T}_{\mathrm{hs}},{V}_b\right)=\frac{E\left({T}_{\mathrm{hs}},{V}_{\mathrm{a},0},{V}_{\mathrm{b},0}\right)E\left({V}_a,{T}_{\mathrm{hs},0},{V}_{b,0}\right)E\left({V}_b,{A}_{a,0},{T}_{hs,0}\right)}{c_2}$$
(5)

The experimental results of the illuminance behavior of the LED are related to bias voltage with constant amplification factors and frequency. It can be seen that illuminance curve is similar with Fig. 4. In practice, the illuminance E is approximately nonlinearly proportional to the bias voltage Vb at constant amplification factors Af,0 and constant frequency f0, so it can be given as

$$E\left({V}_b,{A}_{\mathrm{f},0},{f}_0\right)={\delta}_1{V_b}^2+{\delta}_2{V}_b+{\delta}_3$$
(6)

Where δ1, δ2, and δ3 are coefficients that can be extracted from experimental results of the illuminance as a function of the LED bias voltage with constant amplification factors and frequency.

Figure 5 shows the practical measurements of the illuminance E as a function of the LED amplification factors Af, with constant bias voltage Vb,0 and constant frequency f0. Therefore, the illuminance can be expressed as

$$E\left({A}_{\mathrm{f}},{V}_{b,0},{f}_0\right)={\varepsilon}_1{A}_{\mathrm{f}}+{\varepsilon}_2$$
(7)
Fig. 5
figure 5

Illuminance versus amplification factors of LED device under “constant bias voltage and constant frequency” operation

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Where ε1 and ε2 are coefficients that can be extracted from Fig. 5.

Based on the above analysis, E can be related to amplification Af and bias voltage Vb using a two-dimensional function. Combined (6) and (7), illuminance of the LED device with bias voltage and amplification factors with constant frequency can be given as

$$E\left({A}_{\mathrm{f}},{V}_b,{f}_0\right)=\frac{E\left({A}_{\mathrm{f}},{V}_{b,0},{f}_0\right)E\left({A}_{\mathrm{f},0},{V}_b,{f}_0\right)}{c_3}$$
(8)

Where c3 is intersection values of (6) and (7). It should be pointed out that this model can estimate the illuminance variation of the LED at any bias voltage and amplification factors with constant frequency. Equation (8) links the illuminance to bias voltage and amplification factors together.

Figure 6 shows the practical measurements of the illuminance E as a function of the LED frequency f with constant bias voltage Vb,0 and constant amplification factors Af,0. Therefore, the illuminance can be expressed as

$$E\left({A}_{\mathrm{f},0},{V}_{b,0},f\right)={\mu}_1{f}^2+{\mu}_2f+{\mu}_3$$
(9)
Fig. 6
figure 6

Illuminance versus frequency of LED device under “constant bias voltage and constant amplification factors” operation

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Where μ1, μ2, and μ3 are coefficients that can be extracted from the practical measurements of the illuminance as a function of the frequency with constant amplification factors and bias voltage, as shown in Fig. 6.

Combined with (8) and (9), illuminance of the LED device with bias voltage, amplification factors and frequency can be given as

$$E\left({A}_{\mathrm{f}},{V}_b,f\right)=\frac{E\left({A}_{\mathrm{f},0},{V}_{b,0},f\right)E\left({A}_{\mathrm{f}},{V}_{b,0},{f}_0\right)E\left({A}_{\mathrm{f},0},{V}_b,{f}_0\right)}{c_4}$$
(10)

Where c4 is intersection values of function of (8) and (9). It should be pointed out that this equation can estimate the illuminance of the LED at any bias voltage, amplification factors and frequency. Equation (10) links the illuminance to bias voltage, amplification factors and frequency together.

Combined with (5) and (10), the illuminance as function of the LED device with five-dimensional parameters can be determined as

$${\displaystyle \begin{array}{l}E\left({V}_a,{T}_{\mathrm{hs}},{V}_b,{A}_f,f\right)=\frac{\left[\frac{E\left({T}_{\mathrm{hs}},{V}_{\mathrm{a},0},{V}_{\mathrm{b},0}\right)E\left({V}_a,{T}_{\mathrm{hs},0},{V}_{b,0}\right)E\left({V}_b,{A}_{a,0},{T}_{hs,0}\right)}{c_2}\frac{E\left({A}_{\mathrm{f},0},{V}_{b,0},f\right)E\left({A}_{\mathrm{f}},{V}_{b,0},{f}_0\right)E\left({A}_{\mathrm{f},0},{V}_b,{f}_0\right)}{c_4}\right]}{c_5}\\ {}=\frac{\left[\frac{E\left({T}_{\mathrm{hs}},{V}_{\mathrm{a}},{V}_{\mathrm{b}}\right)}{c_2}\frac{E\left({A}_{\mathrm{f}},{V}_b,f\right)}{c_4}\right]}{c_5}\end{array}}$$
(11)

Therefore, the overall illuminance of a mixed white LED device Et(Va,t,Ths,t,Vb,t,Af,t, ft) with a cool white LED and a warm white LED is shown as Eq. (12)

$${\displaystyle \begin{array}{l}{E}_t\left({V}_{a,t},{T}_{\mathrm{hs},\mathrm{t}},{V}_{b,t},{A}_{f,t},{f}_t\right)={E}_c\left({V}_{a,c},{T}_{\mathrm{hs},\mathrm{c}},{V}_{b,c},{A}_{f,c},{f}_c\right)+{E}_w\left({V}_{a,w},{T}_{\mathrm{hs},\mathrm{w}},{V}_{b,w},{A}_{f,w},{f}_w\right)\\ {}=\frac{\left[\frac{E_c\left({T}_{\mathrm{hs},\mathrm{c}},{V}_{\mathrm{a},\mathrm{c}},{V}_{\mathrm{b},\mathrm{c}}\right)}{c_{2,\mathrm{c}}}\frac{E\left({A}_{\mathrm{f},\mathrm{c}},{V}_{b,c},{f}_c\right)}{c_{4,\mathrm{c}}}\right]}{c_{5,c}}+\frac{\left[\frac{E_w\left({T}_{\mathrm{hs},\mathrm{w}},{V}_{\mathrm{a},\mathrm{w}},{V}_{\mathrm{b},\mathrm{w}}\right)}{c_{2,\mathrm{w}}}\frac{E\left({A}_{\mathrm{f},\mathrm{w}},{V}_{b,w},{f}_w\right)}{c_{4,\mathrm{w}}}\right]}{c_{5,w}}\end{array}}$$
(12)

Where Φc(Va,c,Ths,c,Vb,c,Af,c,fc) is individual illuminance of the cool white LED and Φw(Va,w,Ths,w,Vb,w,Af,w, fw) is individual illuminance of the warm white LED.

Several important observations should be pointed out from Eq. (12):

  1. (1)

    Equation (12) relates the illuminance to the heatsink temperature Ths, frequency f, amplitude voltage Va, bias voltage Vb and amplification factors Vf altogether. It is an equation that integrates the heatsink temperature and driver parameters of the LED device altogether.

  2. (2)

    LED device manufactures can use heatsink temperature Ths, frequency f, amplitude voltage Va, bias voltage Vb and amplification factors Vf in Eq. (12) to quantify the overall illuminance of a mixed white LED device. This new equation quantitatively sums up the relationship of illuminance, heatsink temperature Ths, frequency f, amplitude voltage Va, bias voltage Vb and amplification factors Vf.

  3. (3)

    The required parameters of the proposed model are calibrated from a series of measurement as shown in Figs. 2, 3, 4, 5, and 6.

Results and discussion

In the experiments, a cool white LED (CREE-XPE 1W) and a warm white LED (CREE-XPE 1W) making up the mixed white LED sources is mounted on a temperature-controllable heatsink. The rated CCT of the cool white and warm white LED are 5000 K and 2900 K respectively. The descriptions have been added above Fig. 7. Figure 7 shows the schematic of experimental setup. The light flicker analyzer (FA-3000) shows the waveform of the light output of the LED system with a sinusoidal wave of a given parameters (frequency: 100 Hz, heatsink temperature: 25 °C, amplitude voltage: 6 V, bias voltage: 2 V, amplification factors: 5 dB). A high power mixed white LED was electrically driven with different heatsink temperature. A wide band amplifier (Texas Instruments ATA-122D) adds the signal function (Gigol DG5071) to the DC component coming from DC power supply. The signal amplifying function with high speed is injected into the LED. The light output of the LED was captured from detector (FA-3000). The heatsink temperature is from 25 °C to 85 °C. The voltage amplitude is from 5 V to 9 V. The bias voltage is from 1 V to 5 V. The amplification factors are from 4.5 to 7.5. The frequency is from 100 Hz to 2000 Hz.

Fig. 7
figure 7

Schematic of experimental setup

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The illuminances of LED source are measured through the dark-tube, as shown in Fig. 7. The LED source is connected to photodetector by the dark-tube. The distance between the source and photo detector is 20 cm. Therefore, the environments have not influence on measured results of photodetector. The measured optical performance of the mixed white LED source is dependent on the responsivity for the photodetector and the spectral power distribution of the LED source. Fig 8 shows responsivity of the photodetector and spectral power distribution of LED source with different current. It is clearly shows that the responsivity for the photodetector is different from wavelength distribution. The spectral power distribution of LED source exhibit variation due to thermal and electrical factors. As shown in Eqs. (1) and (12), the signal-to-noise ratio and illuminance of the LED source is highly related to spectral power distribution of LED source.

Fig. 8
figure 8

Responsivity of photodetector and the spectral power distribution of the white LED sources with electrical-thermal effects

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The illuminance of cool white LED and warm white LED is measured at different heatsink temperature Ths, frequency f, amplitude voltage Va, bias voltage Vb and amplification factors Vf. The required coefficients of cool white LED and warm white LED in Eq. (12) can be extracted in Tables 1 and 2.

Table 1 Required coefficients for proposed model of cool white LED
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Table 2 Required coefficients for proposed model of warm white LED
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Putting coefficients of Tables 1 and 2 into Eq. (12), the theoretical illuminance Et(Va,t,Ths,t,Vb,t,Af,t,ft) with different heatsink temperature Ths, frequency f, amplitude voltage Va, bias voltage Vb and amplification factors Vf can be determined. The illuminance is measured at different operation conditions. The theoretical and measured illuminance curves are measured and shown in Figs. 9, 10, and 11. The theoretical results have good agreement with experiment result in Fig. 9 for a set of heatsink temperature, voltage amplitude, and bias voltage. The average deviation between the calculations and the measurements are about 7.9%. The maximum deviation between the calculations and the measurements are 13.6%. For experiments, a temperature-controlled heatsink is adjusted to control heatsink temperature of LED sample. The LED sources consist of multiplicity conductor materials. The temperature-controlled heatsink could not provide high-precision control on the junction temperature. It means that the practical junction temperature may be lower than target value due to imperfect heat flow path. That is major cause of errors between the calculations and measurements of Fig 9.

Fig. 9
figure 9

a Calculated illuminance of the mixed white LED source with heatsink temperature, bias voltage, and voltage amplitude. b Measured illuminance of the mixed white LED source with heatsink temperature, bias voltage, and voltage amplitude

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Fig. 10
figure 10

a Calculated illuminance of the mixed white LED source with amplification factor, bias voltage, and voltage amplitude. b Measured illuminance of the mixed white LED source with amplification factor, bias voltage, and voltage amplitude

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Fig. 11
figure 11

a Calculated illuminance of the mixed white LED source with frequency, bias voltage, and voltage amplitude. b Measured illuminance of the mixed white LED source with frequency, bias voltage, and voltage amplitude

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Based on coefficients in the Tables 1 and 2, the illuminance of the mixed white LED as a function of amplification factor, bias voltage and voltage amplitude is calculated using (12) and plotted in Fig. 10. In general, the calculated results are consistent with the practical measurements. The average deviation between the theoretical and experimental results is about 8.9%.

The measured and calculated illuminance of the mixed white LED source with frequency, bias voltage and voltage amplitude are shown in Fig. 11. The theoretical curves of illuminance are in good agreement with the measured ones. Given a constant bias voltage 4 V and voltage amplitude 5 V, it is important to note that at a controlled frequency of 100 Hz, illuminance is about 985.5 lx. When the frequency is 1000 Hz, illuminance decreases to 860.5 lx. It is noted that illuminance decreases with increasing operating frequency under constant power.

Figure 12 shows the calculated and measured SNR of the mixed white LED sources with frequency, bias voltage and voltage amplitude. The calculated values using the proposed model are generally consistent with the measurements. The average deviation between the theoretical and experimental results is about 13.5%. The variation SNR of the mixed white source with the bias voltage of 1V and voltage amplitude of 5 V is about 10.1% from frequency of 100 Hz to 2000 Hz. It is noted that the variation of SNR with frequency and voltage amplitude are kept within obvious ranges.

Fig. 12
figure 12

a Calculated SNR of the mixed white LED source with frequency, bias voltage and voltage amplitude. b Measured SNR of the mixed white LED source with frequency, bias voltage and voltage amplitude

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Conclusions

Currently, the LED optical model is investigated with DC, PWM, bi-level, and n-level driver. Actually, the optical performance for traffic light is related to sinusoidal waveform driver. In other words, the optical performance and SNR of traffic source using by LED device can be affected by sinusoidal waveform driver. There is still a lack of understanding on such aspects, which are important for the optimization of the traffic light design. In this paper, we attempted to develop a five-dimensional model to study sinusoidal waveform driver and heatsink temperature effects on illuminance and SNR performance of traffic light with LED source. A prediction method for the illuminance and SNR of the mixed white LED source with a warm white LED source and a cool white LED source as function of heatsink temperature, frequency, amplitude voltage, bias voltage and amplification factors is proposed in this paper. The proposed model can estimate the illuminance and SNR with different heatsink temperature and driver parameters. The proposed model cover extends the illuminance and SNR of LED source inside smart traffic information system to include the key parameters of sinusoidal waveform. In general, the calculated results using by the proposed model are consistent with the practical measurements. The average deviation between the theoretical and experimental illuminance and SNR with different conditions is about 8.9% and 13.5% respectively. It is pointed out that the proposed model can be used as a design tool for traffic designs. LED manufacturers are encouraged to provide more results such as illuminance and SNR as a function of frequency, bias voltage, amplification factors and amplitude voltage in the datasheets as basic coefficients for LED system designs for traffic information system. It should be pointed out that required parameters of the proposed modeling are specific parameters for traffic light using by LED source. The re-calibration measurements should be carried out if the traffic light is used by the different type of LED.