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# Integrated Circuit Interface for SAW Biosensors Applications

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Chapter 5: Simulation results of the SAW interfacing circuit 78

Figure 5- 14 Counter transitions at clock rising edge

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Chapter 5: Simulation results of the SAW interfacing circuit 79

Figure 5- 15 Counter output at one complete Enable cycle

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Chapter 5: Simulation results of the SAW interfacing circuit 80

5.5 Power consumption

The circuit power consumption is divided into two parts: analogue and digital. The
analogue power consumption is due to the oscillators, the mixer and the analogue
cells. The digital conversion of the square wave produces the digital power
consumption. The oscillator simulated DC power is shown in figure 5-16.

Figure 5- 16 Oscillator DC power

Each oscillator consists of two amplifiers. Each consumes an average of
6.2mW. The two inverters consume 3.6mW each. The oscillator buffer average
power consumption is 3.4mW. Adding all together, 23mW are dissipated in each
oscillator to produce a total of 46mW. It is noticed that the maximum power
dissipation occurs at the minimum temperature (20°C). The mixer DC power is
shown in figure 5-17. The mixer output DC component adds 6mW as shown in
mixer transient analysis (figure 5-8). The mixer maximum power consumption is
2.7mW + 6mW = 8.7mW. The circuit contains band-gap, biasing and comparator
cells. From Appendixes A.3.1 and A.3.2, the DC currents of the band-gap, biasing
cells are 29µA and 6.5µA respectively. They contribute (35.5µA) × (5V) ≈ 0.2mW.
The comparator current is 73µA when enabled and 3µA when disabled (Appendix
A.3.3). The square wave duty cycle is about 35% so its power dissipation is about
(5V × (73µA×0.35+3µA)) ≈ 0.15mW. The total analogue power consumption is
calculated to be (46mW + 8.7mW+ 0.2mW + 0.15mW) 54mW.

The digital circuit power consumption is calculated according to the
following equation (neglecting static power):

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Chapter 5: Simulation results of the SAW interfacing circuit 81

fclk is the clock frequency

VDD is the supply voltage

Fswitch the circuit switching factor (<1)

P = f���V
��

C���� F�����h

Figure 5- 17 Mixer DC power

Since the number of transistors is in the range of hundreds and the maximum
clock frequency is 10kHz; the total power dissipation is negligible for gate
capacitance in the range of Pico farads. From the preceding analysis, the total circuit
power consumption is about 55mW. This power will affect the chip temperature.
From figure 4-21 in section 4.5, it can be seen that this amount of power will heat the
chip by an average of 5°C.

5.6 Temperature effect

The Temperature Coefficient of Frequency (TCF) of the SAW resonator depends on
its piezoelectric substrate material. For the lithium tantalate substrates; the TCF is
about -20ppm/Hz. The effect of temperature is modelled in the SAW motional
capacitance.

The resonator frequency f0 at a reference temperature is calculated as:

=

��

eq.5.5

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Chapter 5: Simulation results of the SAW interfacing circuit 82

At one degree temperature above the reference temperature, the resonant
frequency f1 is calculated as shown in equation 5.6

=

��(�∆�)

eq.5.6

ΔCm is the motional capacitance difference

The frequency difference Δf = f0 f1 is shown in the following equation:

∆푓 =

��

���∆�

=

��

( 1

���
∆�

) eq.5.7

Substituting the approximation (1+x)-1/2
(ΔCm/Cm) <<1)
≈ 1-0.5x at x<<1 (in this case

∆푓 =

��

0.5 ∆�

eq.5.8

Re-arranging and substituting using f0

∆�

= 0.5 ∆�

eq.5.9

For 20ppm change at 1°C; the ratio between the motional capacitance variation
to the reference motional capacitance is Cm/Cm= 40 × 10-6.

So modelling the motional capacitance as 4fF capacitor with a first order
temperature coefficient of 40 × 10-6 will give the temperature effect.

Figure 5-18 shows the oscillator resonant frequency over a temperature range
from 20°C to 50°C

It can be seen that SAW oscillator output exhibits a linear decrease with
temperature. The slope of the frequency variation with temperature is calculated as

푆푙표푝푒 = (���.�������.���)���
��°= 6.83 푘퐻푧eq.5.10

Dividing by the resonant frequency at reference temperature to get the
temperature sensitivity

푆푒푛푠푖푡푖푣푖푡푦 = �����

=

.�� ���

���.����

≅ −30푝푝푚 eq.5.11

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Chapter 5: Simulation results of the SAW interfacing circuit 83

Figure 5- 18 The SAW oscillator frequency change versus temperature

The increase in temperature negative sensitivity from -20ppm to -30ppm is due
the oscillator circuit amplifier temperature effect. The mixer is the first step in
temperature compensation. Each of the reference and the sensing oscillators will
have -30ppm decrease in its output frequency; consequently, the mixer output
frequency will be constant at different temperatures.

Figure 5- 19 Mixer output at temperature range from 20°C to 50°C

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Chapter 5: Simulation results of the SAW interfacing circuit 84

The mixer output frequency was simulated over a temperature range between
20°C and 50°C. The PSS simulation results are shown in figure 5-19.

From the results it can be seen that the mixer output frequency remains
constant over the entire temperature range.

5.7 Temperature Control

While the previous section shows that the digital output is independent of
temperature due to the elimination of the temperature effect by using the mixer, it is
very beneficial to control the SAW device and circuit temperature to have stable
measurements and more accurate results.

The temperature control mechanism is designed using a digital logic feeding a
MOSFET gate as shown in figure 4-17. The default values of the temperature and
the heater resistance are assumed to be 27°C and 25Ω respectively. The control logic
uses the default values if the calibration is not done manually. Manual calibration is
done by setting the Calibrate_EN signal to high. The logic can process the inputs
when the Activate clock signal is high. The Activate signal can be manually turned
high before the input signal is applied. The input is applied serially to feed the
system with the required temperature and heater resistance.

The heater resistance is entered first in 16 consecutive inputs in Binary Coded
Decimal (BCD) format starting with the most significant bit. For instance, when
25.65Ω is required; the entered BCD value is Hex-Decimal (2565) which is
equivalent to the serial binary sequence of (0010 0101 0110 0101). After entering the
required resistance; the required temperature is entered in the serial input in 12 bits.

The same method is applied. Figure 5-20 shows the simulation of the
calibration process using the heater resistance and temperature values as 25.65Ω and
27.3°C respectively.

It can be noticed that the temporary registers for the reference resistance and
temperature Rh0 and T0 values are set to their default values (25Ω and 27 °C) after
the asynchronous reset (Rst=1). The register values are in Hexadecimal format
(Rh0=H’3D090’, T0=’A8C’). These values equal the original values multiplied by
10000 and 100, respectively. After the calibration is done; the Calibrate_EN is
turned down. At its falling edge; the system stores the calibrated values of the
resistance and temperature in the corresponding registers Rh0 and T0 as shown in the
simulation results. The new values are H’3E9F4’ and H‘AAA’. These values are
equivalent to the decimal of 256500 and 2730 to produce the equivalent of the
25.65Ω and 27.3°C.

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Chapter 5: Simulation results of the SAW interfacing circuit 85

Figure 5- 20 Temperature control calibration process

The asynchronous reset of the logic circuit assumes that the control voltage of
the gate is equal to 3V. On a 10-bit Analogue to Digital Converter (ADC) scale with
reference voltage of 5V; this value is translated as shown in equation 5.12.

��� = × ��

eq.5.12

VADC is the ADC output voltage and Va is the analogue voltage.

Substituting in equation 5.12 with the default control voltage 3V yields:

��� = × ��

= 퐵 ′1001100110eq.5.13

The B symbol indicates a binary value.

Figure 5-21 illustrates the asynchronous reset process. After the asynchronous
reset (Rst=’1’); the control voltage is assumed to have its default binary value
B‘1001100110’ which corresponds to the hexadecimal value of H’266’.

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Chapter 5: Simulation results of the SAW interfacing circuit 86

Figure 5- 21 Temperature control logic status after asynchronous reset

The assumed indicated values of the heater and poly voltages (VH_ADC and
HP_ADC) are H’0CA’ and H’0DA’ respectively. On a 5V 10-bit ADC; this
corresponds to VH=0.987705V and VP=1.065603V. The preceding values are
extracted from the analogue simulation at 25.4°C. Substituting in equation 4.27 gives
the same heater value.

The calculation of temperature coefficients of both heater and poly resistance
(alpha_h, alpha_p) are enabled after the Enable signal goes high. This is shown in
figure 5-22. Both the power-temperature relationship constants A, B are initiated
after the Enable signal is turned to logic 1. The same applies to the default poly
resistance RP0. Their hexadecimal values correspond to their decimal equivalents as
shown below.

alpha_h= 6 × 10-3/ °C => H’3C’
The value is multiplied by 10000 for further processing.

alpha_p=0.2 × 10-3/ °C => H’02’
The value is multiplied by 10000 for further processing.

RP0= 2.0059Ω => H’4E5B’.

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Chapter 5: Simulation results of the SAW interfacing circuit 87

The value is multiplied by 10000 for further processing.

A= 17.9472=> H’ 02BD10’

B= -0.9329=> H’FFFF3A’

Multiplied by 10000

In two’s complement form multiplied by 10000

Figure 5- 22 Temperature control logic voltage enabled

After the Enable signal is high; the system waits the rising edge of the clock
signal. At such a rising edge, the system computes the current resistance and
temperature in the temporary registers Rh and T respectively. The Rh value is
H’03DDA1’ which corresponds to the decimal of 253345 (25.33Ω). The difference
between the computed and the original values (25.65Ω as stated earlier) is due to the
computation algorithm. The computed value of temperature T is H’09DD’ which is
equivalent to 25.3°C (a 0.1°C shift from the actual value).

After the temperature calculation; the required control voltage is calculated.
The simulation of this process is shown in figure 5-23. The control voltage
(Vctrl_DAC) is changed from its default value (3V) corresponding to H’266’ to the
value of H’34C’ which is converted to an analogue voltage of 4.12V according to
equation 5.12