# Integrated Circuit Interface for SAW Biosensors Applications

Chapter 5: Simulation results of the SAW interfacing circuit 78

Figure 5- 14 Counter transitions at clock rising edge

Chapter 5: Simulation results of the SAW interfacing circuit 79

Figure 5- 15 Counter output at one complete Enable cycle

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):

Chapter 5: Simulation results of the SAW interfacing circuit 81

f_{clk }is the clock frequency

V_{DD }is the supply voltage

C_{load }is the load capacitance

F_{switch }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 f_{0 }at a reference temperature is calculated as:

푓

� ^{=}

�

��_{�}�_{�}�_{�}

eq.5.5

Chapter 5: Simulation results of the SAW interfacing circuit 82

At one degree temperature above the reference temperature, the resonant

frequency f_{1 }is calculated as shown in equation 5.6

푓

� ^{=}

�

��_{�}�_{�}(�_{�}�∆�_{�})

eq.5.6

ΔC_{m }is the motional capacitance difference

The frequency difference Δf = f_{0 }– f_{1 }is shown in the following equation:

∆푓 =

�

��_{�}�_{�}�_{�}

−

�

��_{�}�_{�}�_{�}�∆�_{�}

=

�

��_{�}�_{�}�_{�}

( 1 −

�

���

∆�_{�}

�_{� }^{�}

�

�

) eq.5.7

Substituting the approximation (1+x)^{-1/2}

(ΔC_{m}/C_{m}) <<1)

≈ 1-0.5x at x<<1 (in this case

∆푓 =

�

��_{�}�_{�}�_{�}

�0.5 ^{∆�}^{�}�

�_{�}

eq.5.8

Re-arranging and substituting using f_{0}

∆�

�_{�}

= 0.5 ^{∆�}^{�}

�_{�}

eq.5.9

For 20ppm change at 1°C; the ratio between the motional capacitance variation

to the reference motional capacitance is ∆C_{m}/C_{m}= 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 푘퐻푧/°퐶 eq.5.10

Dividing by the resonant frequency at reference temperature to get the

temperature sensitivity

푆푒푛푠푖푡푖푣푖푡푦 = ^{�����}

�_{�}

=

�.�� ���/°�

���.����

≅ −30푝푝푚 eq.5.11

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

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.

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.

푉_{��� }_{= }�_{�}× �^{��}

�

eq.5.12

V_{ADC }is the ADC output voltage and V_{a }is the analogue voltage.

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

푉_{��� }_{= }�_{�}× �^{��}

�

= 퐵 ′1001100110′ eq.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’.

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’.

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