CHAPTER 1 INTRODUCTION
1.2 RESEARCH MOTIVATION AND ORGANIZATION OF THIS THESIS 4
1.2.2 THESIS ORGANIZATION
This thesis is divided into four chapters. The first chapter introduces the background and motivation of this thesis. The architecture and the circuit design of the chip are elaborated in the following chapter. Simulation results of both the biological model and the circuit are also presented in this chapter. Chapter 3 shows the layouts of the chip and the measurement results. In the last chapter, we draw conclusions and bring up the direction of future works.
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Fig. 1. Cross section of the human eye. The gray arrow shows the path of light through the optical apparatus. Reprinted from “Fundamental Neuroscience,” by D. E. Haines,
2002, p. 304
Fig. 2. The cross section of the human retina. The labels c, r, h, b, a, and g indicate cones, rods, horizontal cells, bipolar cells, amacrine cells, and ganglion cells respectively.
Reprinted from “Fundamental Neuroscience,” by D. E. Haines, 2002, p. 306.
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Fig. 3. Interactions in the outer plexiform layer of the retina. Label C, H, and B indicate cone, horizontal cells and bipolar cell respectively. Reprinted from [6].
BipolarON
Bistratified OnBriskTrN OnSluggish OffBriskTr OffBriskL OnBeta
Photo-input
Fig. 4. The CNN model of outer and inner plexiform layer including cone cells, horizontal cells, bipolar cells, amacrine cells, and ganglion cells. The horizontal line represents a kind of neuron type. Vertical line indicates an interaction between layers.
Reprinted from [7].
7 Photo-input
G=4 τ=20
G=-1.5 D=10
τ=60
τ=22 D=150
PH2
Output PH1
Horizontal
Fig.5. Equivalent block diagram of the outer retina in the CNN model. D and τ represent space and time constant respectively. The units for D and τ are µm and ms respectively.
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CHAPTER 2
CIRCUIT DESIGN OF THE RETINAL CHIP
2.1 ARCHITECTURE OF A BASIC CELL OF THE RETINAL CHIP
In our design, a number of identical basic cells in an array constitute the retinal chip.
The basic cell is designed following the previously mentioned model derived from biological measurements of the photoreceptor and horizontal cell. The block diagram of the model is shown in Fig.5. In this model, there are two coefficients. τ is the time constant and D is the diffusion constant, also called space constant. τ and D are important parameters of spatio-temporal characteristics of the retina. However each parameter in the model is a relative quantity rather than a fixed one. Actually biological measurement results vary with different test samples. Therefore, our design is focused on realizing comprehensive spatio-temporal characteristics instead of realizing precise coefficients in the model. Thus the actual architecture of the basic cell is slightly
modified to the one shown in Fig. 6. The main difference between the actual architecture and the original CNN-model one is that the time constants of PH1 and horizontal are neglected because they are about the same. Besides, the space constant of PH1 is also neglected for its small quantity with respect to that of horizontal.
As shown in Fig. 6, there are four major parts in a basic cell, namely, photo-input, photoreceptor-1 (PH1), photoreceptor-2 (PH2), and horizontal (Horizontal). Photo-input, PH1, and PH2 together realize the function of the biological photoreceptor.
Photo-input acquires incident signal which is delivered to the other parts of the cell for processing. The PH1 subtracts the output of PH2 and the horizontal from that of the photo-input and makes the result the output of the whole cell.
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The PH2 acts as a low-pass filter whose input is the output of PH1. PH2 then feeds the low-passed signal back to PH1 for subtraction. If a pulse signal like the one in Fig.
7(a) is applied as the photo-input, the output of PH2 will be like the curve in Fig. 7(c), and then the output of the cell overshoots at the rising edge and undershoots at the falling edge as sketched in Fig. 7(b). This phenomenon obviously arises from the subtraction operation at PH1 and the low-pass operation at PH2.
The horizontal mimics the horizontal cell in real retina to perform diffusion of PH1’s signal and feed the diffused signal back to PH1 for subtraction. The horizontal, in fact, realizes the smoothing or blurring function in spatial domain. As illustrated in Fig. 8, (a) is the incident pattern and (b) is the result after the horizontal operation. The six center cells are turned on and the others are turned off. The subtraction at PH1 makes the final output a Mexican-hat-like pattern shown in Fig. 8(c). It could be noticed that the output of PH1 is lowered in the turned-off side and heightened in the turn-on side.
Therefore the contrast at the edge is increased with compared to the incident pattern. The processing of horizontal and PH1 enhance the edge of the incident image and make the original image clearer.
Fig. 7 and Fig. 8 are the simulated results of the model in Fig. 6. Thirty-two cells constructed according to the model are connected in series to form a 1-D array. The
function of PH2 is implemented by a single-pole low-pass filter with the transfer function of
The horizontal is achieved by a normalized template that is a discretely sampled Gaussian function in the form
( )
template, µ the center of the template, and σ is the diffusion constant. The horizontal output of each cell is the weighted average of its input and adjacent cells’ inputs. The weighing is the Gaussian template presented above. This template controls the diffusion extent of the horizontal. σ is the controlling parameter. With a larger σ, the input10
signal could be diffused further. The above and following model simulations are
performed using the elements above and the simulation tool is MATLAB Simulink. Fig.
9 shows the influence of varying diffusion constant on the transient response of the model.
The middle six cells are turned on for some time and turned off rapidly. The results in Fig.
9 are the outputs from the most center cell. First examine the transient of the horizontal in Fig. 9(c). It could be found that the both of steady-state value and shootings are lower when a larger σ is applied. This is due to the fact that a larger σ makes output of the horizontal the average of a lager area. The signal at one cell could diffuse out further.
Therefore the horizontal output of the turned-on cell is averaged to a smaller quantity.
Since the output of PH1 plus that of PH2 is the result of subtracting horizontal from photo-input, a smaller horizontal output would make larger PH2 and PH1. As shown in Fig. 9(a), the steady-state value of PH1 increases with the increasing diffusion constant and so does PH2
The simulation result of varying time constant of PH2 is shown in Fig. 10. With a larger time constant, both of PH1 and PH2 need more time to reach their steady state values, but their steady state values are independent of time constant. Fig. 11 shows the simulated spatial response of PH1 and horizontal. It could be found that space constant
σ controls the diffusion range. A larger σ makes a wider diffusion area.
2.2 CIRCUIT DESIGN OF THE BASIC CELL
Fig. 12 shows the circuitry design for the modified architecture mentioned in previous section. The dimensions of all of the devices in this circuit are listed in Table I.
The circuitry is described in detail in the following.
2.2.1 THE PHOTO-INPUT
The photo-input is a phototransistor together with a current conveyer used to transduce the incident light into current. The phototransistor is just a parasitic vertical PNP bipolar junction transistor (BJT) in the standard CMOS process with its base floated as represented by Q1. The base region is used to sense the incident light and generate the
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photocurrent. When the light is incident upon the open-base region of the photo-BJT, carriers in this region are generated and photocurrent appears at the emitter. The depletion region of the collector junction has a greater efficiency in generating the carriers for its reverse bias condition when the BJT is in forward active region [9].
Another component in photo-input, current conveyor, is realized by MP1, MP2, MN1, MN2, MN3, and MN12. Current conveyor is a three-port component, as shown in Fig. 13. Fig. 13(a) is the block diagram of a current conveyor. This current conveyor is described by
An implementation of current conveyor we use in our design is placing a NMOS transistor in the negative feedback loop of an operational amplifier, as shown in Fig.
13(b). In this configuration, the voltage at X follows that applied to Y, and the current supplied to X is conveyed to the high-impedance output terminal Z.[10]
In our circuit, MP1, MP2, MN1, MN2, and MN3 form a differential amplifier used in current conveyor. MN12 is then the NMOS used to convey the current from photo-BJT to the other part of the cell. The current conveyer clamps the emitter of the
phototransistor with a voltage close to Vbias1 to prevent the phototransistor from leaving the forward active region.
When the light is incident on the base-collector junction of the phototransistor, the photocurrent is generated and amplified by the phototransistor. The induced photocurrent is then mirrored to MP4 through the current mirror formed by MP3 and MP4 from which other elements in the cell could exploit the induced photocurrent for further processing.
The transistor MN13 is added in parallel with the phototransistor to provide a constant offset current that is controlled by Vbias4. The photo-input can still work without this offset current. However, during the turn off transient of the incident light the feedback subtractive current from PH2 attempts to force the current of PH1 to be negative as shown in Fig. 7; nevertheless, only when the gate-voltage of MN4, also the drain voltage, be negative could the current of MN4 be negative. Since the source of MN4 is grounded, the lowest allowable voltage of the gate or drain of MN4 is zero. The current is
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impossible to be negative, and the undershooting phenomenon of the cell’s output disappears consequently. Therefore, an additional current source that maintains the operating current in a proper level is necessary to keep proper spatiotemporal
characteristics. The offset current added to the input of the cell by MN13 could be viewed as a virtual background illumination since the same offset currents are added to each cell of the chip as a real background lamination affects the chip. Further discussion about MN13 is presented in the following section.
2.2.2 THE PHOTORECEPTOR-1
A couple of current mirrors are used to realize PH1. The photocurrent with offset added is first mirrored from MP3 to MP4, and then flows through transistor MN4 from which the PH2 and the horizontal element could duplicate just the same current via current mirror pairs MN4-MN5 and MN4-MN8. After that, PH2 and the horizontal element are responsible for low-pass and diffusion operations. The output of the horizontal and PH2 are the drain currents of MN6 and MN10 respectively. These two current signals are copied by two current mirror pairs, MN6-MN7 and MN10-MN11. The drains of MN7 and MN11 are connected with that of MN4, and according to Kirchhoff's current law, the sum of output currents of the horizontal and PH1 plus output of PH1 equals to the output current of photo-input, hence the drain current of MN4 equals to photo-input minus the sum of the horizontal and PH2.
The result of current subtraction at the drain of MN4 is then the output of a single cell. The foregoing operation accomplishes the self-feedback mechanism of
photoreceptors and the feedback mechanism of horizontal cells. In the biological retina, the output of a photoreceptor corresponding to PH1’s output in our design is sent to various kinds of bipolar cells for further processing.
2.2.3 THE PHOTORECEPTOR-2
The function of PH2 is to generate a low-passed signal from PH1’s output with a large time constant coefficient, τ, and then to feed the low-passed signal back to PH1
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for subtraction. This generates undershoot and overshoot waveforms similar to biological measurements.
To realize the architecture, we need a low-pass filter with a large time constant. A circuit named “continuous time current delay element” [11] [12] is used to implement the current-mode low-pass filter. As shown in Fig. 14(a), the current delay element is a current mirror with a capacitor connected between the gates and the sources of the two MOSFET. The small-signal equivalent circuit for this element is sketched in Fig. 14(b).
Here we have neglected the output resistance, ro, and all the parasitic capacitances of each MOSFET. From the equivalent circuit, the transfer function of the delay element is described by
The transfer function validates the low-pass characteristic of the delay element.
According to the equation, the delay element has a time constant of
1 large time constant needed in the biological model, we need a large capacitor which may occupy quite a large silicon area. A common-source amplifier is exploited to save silicon area and to increase fill factor.
The PMOS MP10 with its source and drain tied together is used as a capacitor. To make use of the Miller effect, the capacitor is placed between the input and output of a common-source amplifier constructed by MP8 and MN9 which provides a voltage gain, K. In this way, an enlarged effective capacitance CM' is obtained. The effective capacitance could be described by
) common-source amplifier. If MN9 and MP8 are assumed to be in the subthreshold region,
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the voltage gain K of the common source amplifier could be described by
(
MP MN)
js OX OXIn the above equation, gm,MP8 represent the small signal transconductance of MN8.
COX and C refer to oxide and depletion-region capacitance per unit area respectively. js VT is the thermal voltage. λMP8 and λMN9 are the device parameters of MP8 and MN9.
g represent the small signal transconductance of MN7. About K times silicon area needed to implement the large capacitor without this architecture. However, time constant of this circuit is not absolutely invariable. From equation (8), it could be found that time constant τ is approximately proportional to K and inversely proportional to
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g with CMP10 being regarded as a constant. Actually gm,MP7 are not constant. The small signal transconductance gm,MP7 could be describe as
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when the transistor MP7 is in saturation region, or
OX represent the small signal transconductance and the bias current of MP7 respectively.
COX and C refer to oxide and depletion-region capacitance per unit area respectively. js µP is the mobility of the hole and V is the thermal voltage. If we assume the T
transistors in PH2 are all in sub-threshold region and K is far larger than 1, the time constant could be written as
(
8 9)
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According to (11), the increase of ID,MP7 would raise gm,MP7 and consequently lower the time constant τ . On the contrary, gm,MP7 lowers and τ increases with a smaller bias current ID,MP7. In a word, the constant bias voltage of the circuit could not ensure that the PH2’s time constant keeps constant.
With an enlarged equivalent capacitor, MP7 and MP9 form the delay element mentioned above. Finally, another current mirror pair, MN10 and MN11, is in aid of sending back the low-passed signal to PH1.
2.2.4 THE HORIZONTAL
The horizontal element imitates an essential part of the biological retina, the horizontal cell, to diffuse out the input signal from PH1 directly from one cell to its adjacent neighbors. Each cell in the proposed 2-D retina structure is connected to their neighboring cells through NMOS transistors, MNR and MNL. All these transistors form the rectangle resistive network.
When the current signal acquired from PH1 is delivered to the horizontal element, a four times signal is produced by means of the four times channel width-to-length ratio of the current mirror pair, MP5 and MP6. The amplified current then diffuses through the resistive connection to other cells, and beyond question, the amplified current from vicinal cells could diffuse through the same connection to the very cell simultaneously.
The diffusion process is substantially the same as a smoothing function that perform local average of the input signal. The extent of such average is determined by the resistance of the interconnections between cells, which could be controlled by the gate bias, Vsm, of MNR and MNL. The output of the horizontal element, namely the current flowing through transistor MN6, is ultimately mirrored back to the PH1 as well.
2.2.5 IMPACTS OF DEVICE LEAKAGE AND MISMATCH
Since we use many current mirrors in our circuit, device mismatches may affect the performance of the chip. However, the goal of our chip is to reproduce response of the real retina qualitatively, and therefore the parameters, time constants and space constant,
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are not necessary to be accurate values. As long as the characteristics of the response of the chip, overshooting and undershooting or smoothing function, are ensured to be correct, device mismatched could be tolerated.
Since the photocurrent induced by light is rather small compared to the leakage current of the devices, the input signal must be large enough that the output signal could be observed. If too small input signal is applied, the output current might be affected by leakage currents or noise. The output current might not be observable consequently.
2.3 ARCHITECTURE OF 2-D RETINAL ARRAY
The chip consists of an array of 32x32 pixels, address decoders, and output buffer.
The overall architecture of the chip is shown in Fig. 15.
A number of identical basic cells are arranged to form a rectangular array. Two decoders are used to control the output of the cell. The row decoder decodes the m row address bits and activates one of 2m row control signals. The column decoder decodes the n column address bits and activates one of 2n column control signals. In our design, a 32x32 2-D retina array is designed, and therefore two 5-bit addresses are needed for row and column address to select one cell from all of 32x32 cells. The circuit of the address decoder is shown in Fig. 16. The fundamental block of the address decoder circuit is the five-input and gate. The inputs of each and gate are five non-inverting or inverting address bits, and none of arbitrary two input configurations are the same because an address can only activates one row or one column. The selected address line is set to logic high or the most positive voltage supply of the chip, that is, VDD.
Although the final output of the cell is from PH1, each cell in our chip has four output currents, the output of photo-input, PH1, horizontal, and PH2, because these outputs should also be measured to verify the functions of each block. Fig. 17 shows the read out circuit of each basic cell. Each output current of the cell is first reproduced through current mirror with a gain of five. As shown in Fig. 17, M1 could be MP3, MN4, MN6, or MN10 when the output of photo-input, PH1, horizontal, or PH2 is to be read out.
The width-length ratio of M2 is five times larger than that of M1, and therefore the actual
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output current is five times of the original one. The amplified current is then fed into two series-connected transistors MSW1 and MSW2 controlled by one of the row signals VR
output current is five times of the original one. The amplified current is then fed into two series-connected transistors MSW1 and MSW2 controlled by one of the row signals VR