9.1.1.1 Sensor Frequency

The sensor frequency is calculated with the following equation.

Equation 6.

where

• ƒ_SENSOR is the calculated oscillation frequency with no target present
• L_SENSOR is the inductance of the sense coil or reference coil
• C_TOTAL is sum of external sensor, board parasitic, and pin parasitic capacitances connected to LCOM, refer to Figure 25

9.1.1.2 Sensor Design Procedure

The following procedure should be followed for determining the sensor characteristics:

1. Determine the diameter of coil (d_coil), which should be 3 times larger than the desired switching distance (d_switch)
2. Determine the desired frequency (ƒ_SENSOR) which should be between 300 kHz and 19 MHz
3. Calculate the range of allowable inductance from the following equation:
Equation 7.
where
• L_SENSOR is the inductance of the LSENSE coil or LREF coil
• I_{SENSOR_MAX} is given in the electrical table
4. Calculate the externally placed sensor capacitor:

Equation 8.

where

• C_BOARD is the parasitic capacitance introduced by the board layout (~4 pF for good layout)
• C_{IN_COM} is the parasitic pin capacitance of LCOM specified as 12 pF in the electrical table

9.2.1.1 Design Requirements

Assume a gear with 8 conductive teeth is used in a system to determine flow rate. Determine the maximum speed that can be reliably detected by the LDC0851 using a sensor frequency of 15 MHz.

9.2.1.2 Detailed Design Procedure

To ensure a reliable reading an event must be sampled twice when the gear tooth covers more of the LSENSE coil than the LREF coil (LS<LR) producing a LOW output and equivalently twice when the gear tooth covers more of LREF than LSENSE (LR<LS) producing a HIGH output. The maximum speed can be achieved when the output toggles at a duty cycle rate of 50%. This can be achieved by using a gear where the width of each tooth is the same as the width of the gaps between the teeth. For asymmetric systems, the minimum width of either the gap or the gear tooth determines the maximum detectable speed. For symmetrical systems, the maximum rotational speed that can be reliably detected in revolutions per minute (rpm) for a given number of gear teeth can be determined by the following formula:

Equation 9.

where

• Gear Speed (rpm) is the calculated speed of the gear
• ƒ _SENSOR is the sensor frequency given by Equation 6
• # gear teeth is the total number of events per rotation

A gear with 8 teeth and sensor frequency of 15MHz could reliably measure a gear rotational speed of 6500 rpm.

9.2.1.3 Application Curves

The metal coverage has an inverse relationship to coil inductance. Figure 27 shows the relationship between the output of the LDC0851 and relative inductance of the coils as the gear is rotating.

Figure 27. Angular Position vs Coil Inductance

9.2.2.1 Design Requirements

A push button that is made of flexible material has a conductive target attached to the underside and a contactless solution using the LDC0851 is required for reliability purposes. Determine the coil characteristics as well as the threshold adjust setting if the following conditions are true:

1. The target is made of a conductive material, such as aluminum foil or copper tape
2. The conductive target is circular and measures 10 mm in diameter
3. The resting height of the conductive target is 2.5 mm above the PCB when no button push
4. The maximum travel distance when pressed is 2 mm, leaving an airgap of 0.5mm above the PCB

9.2.2.2 Detailed Design Procedure

To conserve PCB area, a 4 layer stacked coil approach is used with the sense coil on the top 2 layers and reference on the bottom 2 layers. The LDC0851 switching threshold is then determined by following parameters:

1. Conductive Target Size: The best response is achieved when the target area is ≥100% compared to the coil area.
2. Coil diameter: The diameter of the coil should be at least 3x greater than the desired switching distance.
3. ADJ code: Increasing ADJ code linearly scales down the switching distance estimated by Equation 1.

The coil diameter should not exceed the diameter of the conductive target of 10mm in order to keep the target-to-coil coverage ≥100%. Additionally, in order to detect the lightest button pushes where the conductive target rests at a height of 2.5 mm, the coil should be at least 3 times greater giving a minimum size of 7.5 mm. The user may therefore select a coil size between 7.5 mm and 10 mm. A coil diameter of 10mm is chosen for the most flexibility and tuning range. The response versus ADJ code is shown below in Figure 29.

In this example the deflection caused by the button press (∆d) is 2mm. Note that the ∆d must be enough to cross the “Switch ON” threshold and return past “Switch OFF” threshold of the LDC0851 for a given ADJ code to be considered a valid code. Codes 0 through 6 should not be used because the conductive target has already crossed the "Switch ON" thresholds and would always be in the ON state without a button push. Similarly code 15 should not be used because the output would always be in an OFF state regardless of how hard the button is pushed. Therefore codes 8 through 14 are clearly inside the travel distance of the button. Select code 8 to detect light button pushes, code 11 for medium button pushes, or code 14 to only detect strong button pushes. Once the ADJ code is selected based on user preference, set the resistor divider R1 and R2 values according to section Setting the Threshold Adjust Values.

9.2.2.3 Application Curves

Figure 29. Threshold Adjust Design Space for 10mm Coil Example

9.2.3.1 Design Requirements

The LDC0851 is used in a low power, battery operated system to detect when a window is opened. Determine the average supply current of the LDC0851 if following requirements exist:

1. A lifetime of greater than 10 years is required from a single CR2032 battery which supplies the power for the LDC0851.
2. A microcontroller can be used to wakeup the LDC0851 and capture the high/low output state.
3. At least 1 sample per second (ƒ_SAMPLE) is required to detect if the window is open or closed.

9.2.3.2 Detailed Design Procedure

In order to achieve 10 year lifetime out of a single CR2032 battery, the enable pin (EN) of the LDC0851 can be duty cycled to achieve a low average supply current. Refer to Figure 31 to see the three different states of LDC0851 supply current during duty cycle operation. The sum of the Standby, Ramp, and On currents can be used to calculate the average supply current of the LDC0851, which needs to be below 2.5 µA to achieve a 10 year lifetime from a 220 mAh CR2032 battery.

The average supply current can be calculated in the following steps:

1. Select desired system sample rate (ƒ_SAMPLE) based on the given application. In this example, ƒ_SAMPLE is 1 sample per second.
2. Select the sensor characteristics (ƒ_SENSOR, L_SENSOR, C_SENSOR) based on conversion time and current consumption.
   1. ƒ_SENSOR should be increased as much as possible to minimize the conversion time. 10 MHz is chosen as a starting point.
   2. L_SENSOR should be increased as much as possible to decrease the sensor current (I_SENSOR). Based on a reasonable PCB area, 10 µH is a good starting point.
   3. C_SENSOR is calculated to be 34.5 pF from Equation 8 using the inputs above. This makes C_TOTAL equal to 50.5 pF which meets the requirement of greater than 33 pF to be inside the design space.
3. Calculate the average active current:
Equation 10.
where
• ƒ_SAMPLE is the number of samples per second given from step 1. In this example, ƒ_SAMPLE is equal to 1.
• t_CONVERSION is calculated from Equation 2 to give a conversion time of 433 µs.
• I_DD is the total active supply current given by Equation 5 to be 1.587 mA.
• I_ON is the active current consumed by the LDC0851 which comes to be 1.37 µA.
4. Calculate the average ramp current:
Equation 11.
where
• ƒ_SAMPLE is the number of samples per second given from step 1. In this example, ƒ_SAMPLE is equal to 1.
• t_AMT is the active mode transition time given in the electrical table as typically 450µs.
• I_DD is the total active supply current given by Equation 5 to be 1.587 mA.
• I_RAMP is the current consumed by the LDC0851 before a conversion has started which comes to be 0.357 µA.
5. Calculate the average standby current:
Equation 12.
where
• ƒ_SAMPLE is the number of samples per second given from step 1. In this example, ƒ_SAMPLE is equal to 1.
• t_AMT is the active mode transition time given in the electrical table as typically 450µs.
• t_CONVERSION is calculated from Equation 2 to give a conversion time of 433 µs.
• I_SD is the shutdown current of the LDC0851 given in the electrical table as typically 140nA.
• I_OFF is the standby current of the LDC0851 which comes to be 0.140 µA.
6. Calculate the total average supply current:
Equation 13.
where
• I_ON is the active supply current given from Equation 10 to be 1.37 µA.
• I_RAMP is the ramp current given by Equation 11 to be 0.357 µA.
• I_OFF is the standby current given by Equation 12 to be 0.140 µA.
• I_AVG is the average supply current consumed per second which comes to 1.867 µA.
7. Finally the lifetime of the battery can be calculated:
Equation 14.
where
• Battery Capacity is the amount of charge x time that the battery can hold in mAh. This example uses a CR2032 battery with 220 mAh.
• I_AVG is the value reported in Equation 13 to be 1.867 µA.
• Battery Lifetime (years) is how long the battery will last reported in years which comes out to be 13.5 years with the inputs from above.

For example, using a sensor frequency of 10 MHz, sensor inductance of 10 µH, and 1 sample per second yields a lifetime of 13.5 years for a single CR2032 battery.

9.2.3.3 Application Curves

Figure 31. LDC0851 Supply Current vs. Time During Duty Cycle Operation