9.1.1 Theory of Operation

An AC current flowing through an inductor will generate an AC magnetic field. If a conductive material, such as a metal object, is brought into the vicinity of the inductor, the magnetic field will induce a circulating current (eddy current) on the surface of the conductor. The eddy current is a function of the distance, size, and composition of the conductor.

Figure 46. Conductor in an AC Magnetic Field

The eddy current generates its own magnetic field, which opposes the original field generated by the inductor. This effect can be considered as a set of coupled inductors, where the inductor is the primary winding and the eddy current in the conductor represents the secondary winding. The coupling between the windings is a function of the inductor, and the resistivity, distance, size, and shape of the conductor.

To minimize the current required to drive the inductor, a parallel capacitor is added to create a resonant circuit, which will oscillate at a frequency given by Equation 1 when energy is injected into the circuit. In this way, the LDC1101 only needs to compensate for the parasitic losses in the sensor, represented by the series resistance R_S of the LC tank. The oscillator is then restricted to operating at the resonant frequency of the LC circuit and injects sufficient energy to compensate for the loss from R_S.

Figure 47. LC Tank

The resistance and inductance of the secondary winding caused by the eddy current can be modeled as a distant dependent resistive and inductive component on the primary side (coil). We can then represent the circuit as an equivalent parallel circuit, as shown in Figure 48.

Figure 48. Equivalent Parallel Circuit

The value of R_P can be calculated with:

Equation 2.

where

• R_S is the AC series resistance at the frequency of operation.
• C is the parallel capacitance
• L is the inductance

R_P can be viewed as the load on the sensor driver; this load corresponds to the current drive needed to maintain the oscillation amplitude. The position of a target can change R_P by a significant amount, as shown in Figure 49. The value of R_P can then be used to determine the position of a conductive target. If the value of R_P is too low, then the sensor driver will not be able to maintain sufficient oscillation amplitude.

Figure 49. R_P vs Target Distance for a 14 mm Diameter Sensor

9.1.2 RP+L Mode Calculations

For many systems which use the LDC1101, the actual sensor R_P, sensor frequency, or sensor inductance is not necessary to determine the target position; typically the equation of interest is:

These Position equations are typically system dependent. For applications where the Sensor R_P in Ωs needs to be calculated, use Equation 4:

Equation 4.

where

• RPDATA is the contents of RP_DATA_MSB and RP_DATA_LSB (registers 0x21 and 0x22),
• RP_MIN is the value set by RP_MIN in register RP_SET (register 0x01), and
• RP_MAX is the value set by RP_MIN in register RP_SET (register 0x01).

For example, with device settings of:

• RP_MIN set to 1.5 kΩ, and
• RP_MAX set to 12 kΩ.

If RPDATA = 0x33F1 (register 0x21 = 0xF1 and register 0x22= 0x33), which is 13297 decimal, then the sensor R_P = 1.824 kΩ.

If RPMAX_DIS (Register 0x01-b[7]) is set, then the equation is simply:

Equation 5.

Figure 50. LDC1101 R_P Transfer Curve with RPMIN = 1.5 kΩ and RPMAX = 24 kΩ

The sensor frequency in Hz can be calculated from Equation 6:

Equation 6.

where

• ƒ_CLKIN is the frequency input to the CLKIN pin,
• L_DATA is the contents of registers 0x23 and 0x24, and
• RESP_TIME is the programmed response time in register 0x04.

The inductance in Henrys can then be determined from Equation 7:

Equation 7.

where

• C_SENSOR is the fixed sensor capacitance in Farads, and
• ƒ_SENSOR is the measured sensor frequency, as calculated in Equation 6 above.

Figure 51. Inductance vs Normalized Target Distance for an Example Sensor

9.1.3 LDC1101 R_P Configuration

Setting the RP_MIN and RP_MAX parameters is necessary for proper operation of the LDC1101; the LDC1101 may not be able to effectively drive the sensor with incorrect settings, as the sensor amplitude will be out of the valid operation region. The LDC1101EVM GUI and the LDC Excel® tools spreadsheet (http://www.ti.com/lit/zip/slyc137) can be used to calculate these parameters in an efficient manner.

For R_P measurements, the following register settings must be set as follows:

• ALT_CONFIG.LOPTIMAL(register 0x05-bit0) = 0
• D_CONFIG.DOK_REPORT (register 0x0C-bit0) = 0

1. Ensure that the sensor characteristics are within the Sensor boundary conditions:
   1. 500 kHz < ƒ_SENSOR < 10 MHz
   2. 100 pF < C_SENSOR < 10 nF
   3. 1 µH < L_SENSOR < 500 µH
2. Measure the sensor’s resonance impedance with minimal target interaction (R_PD∞). The minimal target interaction occurs when the target is farthest away from the sensor for axial sensing solutions or when the target coverage of the sensor is at a minimum for rotational or lateral sensing. Select the appropriate setting for RPMAX (register 0x01-bits [5:4]):

R_PD∞ ≤ RPMAX ≤ 2R_PD∞

3. Measure the sensor’s resonance impedance with the target closest to the sensor (R_PD0) as required by the application. Select the largest RPMIN setting that satisfies:
   1. RPMIN < 0.8 × R_PD0
   2. If the required RPMIN is smaller than 750 Ω, R_PD0 must be increased to be compliant with this boundary condition. This can be done by one or more of the following:
      1. increasing ƒ_SENSOR
      2. increasing the minimum distance between the target and the sensor
      3. reducing the R_S of the sensor by use of a thicker trace or wire
4. Check if the worst-case Sensor quality factor Q_MIN=RpMIN × √(C_SENSOR/L_SENSOR) is within LDC1101’s operating range:
   1. 10 ≤ Q_MIN ≤ 400
   2. If Q_MIN < 10, for a fixed ƒ_SENSOR, increase C_SENSOR and decrease L_SENSOR.
   3. If Q_MIN > 400, for a fixed ƒ_SENSOR, decrease C_SENSOR and increse L_SENSOR.
   4. Alternatively the user may choose to not change the current Sensor parameters, but to increase Rp_D0.

If the R_P of the sensor is greater than 75 kΩ, R_P measurement accuracy may be improved by setting RPMAX_DIS to 1.

9.1.4 Setting Internal Time Constant 1

R_P Measurements require configuration of the TC1 and TC2 registers. There are several programmable capacitance and resistance values. Set Time Constant 1 based on minimum sensor frequency:

Equation 8.

where

• ƒ_SENSOR-MIN is the minimum sensor frequency encountered in the system; typically this occurs with no target present.
• V_AMP is sensor amplitude of 0.6V,
• R1 is the programmed setting for TC1.R1 (register 0x03-bits[4:0]), and
• C1 is the programmed setting for TC1.C1 (register 0x03-bits[7:6])

The acceptable range of R1 is from 20.6 kΩ to 417.4 kΩ. If several combinations of R1 and C1 are possible, it is recommended to use the largest capacitance setting for C1 that fits the constraints of Equation 8, as this will provide improved noise performance.

9.1.5 Setting Internal Time Constant 2

Set the Time Constant 2 (register 0x03) using Equation 9:

The acceptable range of R2 is from 24.60 kΩ to 834.8 kΩ. If several combinations of R2 and C2 are possible, it is recommended to program the larger capacitance setting for C2 that fits the constraints of Equation 9, as this will provide improved noise performance.

9.1.6 MIN_FREQ and Watchdog Configuration

The LDC1101 includes a watchdog timer which monitors the sensor oscillation. While in active mode, if no sensor oscillation is detected, the LDC1101 will set STATUS.NO_SENSOR_OSC (register 0x20:bit7), and attempt to restart the oscillator. This restart will reset any active conversion.

The watchdog waits an interval of time based on the setting of DIG_CONF.MIN_FREQ (register 0x04:bits[7:4]). The MIN_FREQ setting is also used to configure the startup of oscillation on the sensor. Select the DIG_CONF.MIN_FREQ (register 0x04-bits[7:4]) setting closest to the minimum sensor frequency; this setting is used for internal watchdog timing. If the watchdog determines the sensor has stopped oscillating, it will report the sensor has stopped oscillating in STATUS. NO_SENSOR_OSC (register 0x20-bit7). If the DIG_CONF.MIN_FREQ is set too low, then the LDC1101 will take a longer time interval to report that the sensor oscillation has stopped.

If the DIG_CONF.MIN_FREQ is set too high, then the watchdog may incorrectly report that the sensor has stopped oscillating and attempt to restart the sensor oscillation.

When the watchdog determines that the sensor has stopped oscillating, the LHR conversion results will contain 0xFFFFFF.

9.1.7 RP+L Sample Rate Configuration with RESP_TIME

The RP+L sample rate can be adjusted by setting by DIG_CONF.RESP_TIME (register 0x04:bits[2:0]). The Response time can be configured from 192 to 6144 cycles of the sensor frequency. Higher values of Response time will have a slower sample rate, but produce a higher resolution conversion.

Equation 10.

9.1.8 High Resolution Inductance Calculation (LHR mode)

For many systems which use the LDC1101, the actual sensor frequency or sensor inductance is not necessary to determine the target position. Should the sensor frequency in Hz need to be determined, use Equation 11:

Equation 11.

where

• LHRDATA is the contents of registers 0x38, 0x39, and 0x3A,
• LHROFFSET is the programmed contents of registers 0x32 and 0x33,
• SENSOR_DIV is the contents of LHR_CONFIG.SENSOR_DIV (register 0x34-bit[1:0]), and
• ƒ_CLKIN is the frequency input to the CLKIN pin: ensure that it is within the specified limits of 1 MHz to 16 MHz.

Note that LHR_DATA=0x0000000 indicates a fault condition or that the LDC1101 has never completed an LHR conversion.

The inductance in Henrys can then be determined from the sensor frequency with Equation 12:

Equation 12.

where

• C_SENSOR is the fixed sensor capacitance, and
• ƒ_SENSOR is the measured sensor frequency, as calculated above.

Example with the device set to:

• LHR_OFFSET = 0x00FF (register 0x32 = 0xFF, and 0x33 = 0x00)
• ƒ_CLKIN = 16 MHz
• SENSOR_DIV = b’01 (divide by 2)

and the conversion result is:

LHR_DATA = 0x123456 (register 0x38 = 0x56, register 0x39 = 0x34,register 0x3A = 0x12)

Then entering LHR_DATA = 0x123456 = 1193046 (decimal) into Equation 11:

Equation 13.

Results in ƒ_SENSOR = 2.400066 MHz.

9.1.9 LHR Sample Rate Configuration with RCOUNT

The conversion time represents the number of reference clock cycles used to measure the sensor frequency. The LHR mode conversion time is set by the Reference count in LHR_RCOUNT.RCOUNT (registers 0x30 & 0x31). The LHR conversion time is:

Equation 14.

The 55 is due to post-conversion processing and is a fixed value. The reference count value must be chosen to support the required number of effective bits (ENOB). For example, if an ENOB of 13 bits is required, then a minimum conversion time of 2¹³ = 8192 clock cycles is required. 8192 clock cycles correspond to a RCOUNT value of 0x0200.

Higher values for RCOUNT produce higher resolution conversions; the maximum setting, 0xFFFF, is required for full resolution.

9.1.10 Setting RPMIN for LHR Measurements

Configure the R_P measurement as shown previously for L measurements. If only L measurements are necessary, then the R_P measurement can be disabled by setting:

• ALT_CONFIG.LOPTIMAL(register 0x05-bit0) = 1
• D_CONFIG.DOK_REPORT (register 0x0C-bit0) = 1

Setting these bits disable the sensor modulation used by the LDC1101 to measure R_P and can reduce L measurement noise. When the R_P modulation is disabled, the LDC1101 will drive a fixed current level into the sensor. The current drive is configured by RP_SET.RPMIN (address 0x01:bits[2:0]). The sensor amplitude must remain between 0.25 Vpk and 1.25 Vpk for accurate L measurements. Use Table 36 to determine the appropriate RPMIN setting, based on the variation in sensor R_P. If multiple RPMIN values cover the Sensor R_P, use the higher current drive setting. The equation to determine sensor amplitude is:

Equation 15.

For example, with a sensor that has an R_P which can vary between 2.7 kΩ to 5 kΩ, the appropriate setting for RPMIN would be 3 kΩ (RP_SET.RPMIN = b101). For more information on Sensor R_P and sensor drive, refer to Configuring Inductive-to-Digital-Converters for Parallel Resistance (RP) Variation in L-C Tank Sensors(SNAA221).

9.1.11 Sensor Input Divider

The reference clock frequency should be greater than 4 times the sensor frequency for optimum measurement resolution:

ƒ_CLKIN> 4ƒ_SENSOR-MAX

For higher sensor frequencies, this relationship may not be realizable without the sensor divider. Set the sensor divider to an appropriate value to produce an effective reduction in the sensor frequency:

ƒ_CLKIN> 4ƒ_SENSOR-MAX ÷ SENSOR_DIV

9.1.12 Reference Clock Input

Use a clean, low jitter, 40-60% duty cycle clock input with an amplitude swing within the range of V_DD and GND; proper clock impedance control, and series or parallel termination is recommended. The rise and fall time should be less than 5 ns. Do not use a spread-spectrum or modulated clock.

For optimum L measurement performance, it is recommended to use the highest reference frequency (16 MHz). LHR conversions will not start until a clock is provided on CLKIN.

9.1.13 INTB Reporting on SDO

INTB is a signal generated by the LDC1101 that reports a change in device status. When INTB_MODE.INTB2SDO=1 (register 0x0A:bit7), INTB is multiplexed onto the SDO pin. Once the reporting is enabled, select the desired signal to report by setting INTB_MODE.INTB_FUNC (register 0x0A:bit[5:0]).

Figure 52. SDO/INTB Connection to MCU

For many microcontrollers, the MISO signal on the SPI peripheral cannot provide the desired interrupt functionality. One method to use the INTB functionality is to connect a second GPIO which triggers on a falling edge, as shown in Figure 51. Table 37 describes the signal functionality that can be programmed onto INTB.

Figure 53. Example INTB Signal on SDO

When INTB_MODE.INTB2SDO (register 0x0A:bit7) = 0, the SDO pin is in a Hi-Z state until the 8^th falling edge of SCLK after CSB goes low. When INTB reporting is enabled by setting INTB_MODE.INTB2SDO = 1, after CSB goes low, the SDO pin will go high and remain high until:

• the event configured by INTB_MODE.INTB_FUNC occurs,
• an SPI read transaction is initiated, or
• CSB is deasserted (pulled high)

9.1.14 DRDY (Data Ready) Reporting on SDO

Completion of a conversion can be indicated on the SDO pin by reporting the DRDY signal – there is a conversion complete indicator for the RP+L conversion (RPL-DRDY), and a corresponding conversion complete indicator for the LHR mode (LHR-DRDY).

When LHR-DRDY or RPL-DRDY is reported on SDO, the SDO pin is asserted on completion of a conversion. While in this mode, conversion data can be corrupted if a new conversion completes while reading the output data registers. To avoid data corruption, it is important to retrieve the conversion rates via SPI quicker than the shortest conversion interval, and to ensure that the data is retrieved before a new conversion could possibly complete.

When INTB is reporting RPL-DRDY, if CSB is held low for longer than one conversion cycle, INTB will be deasserted approximately 100 ns to 2 µs prior to the completion of each conversion. The deassertion time is proportional to 1/ƒ_SENSOR.

When INTB is reporting LHR-DRDY, if CSB is held low for longer than one conversion cycle, INTB will assert on completion of the first conversion and remain low – and it will remain asserted until cleared. To clear the LHR_DRDY signal, read the LHR_DATA registers.

Figure 54. Reporting RPL-DRDY on INTB/SDO

Figure 55. Reporting LHR-DRDY on INTB/SDO

Note that the conversion interval for an LHR measurement is asynchronous to the conversion interval for an R_P+L measurement, therefore the LHR-DRDY signal cannot be used to determine when to read R_P+L conversion results, and vice versa.

9.1.15 Comparator Functionality

The LDC1101 provides comparator functionality, in which the RP+L conversion results can be compared against two thresholds. The results of each R_P and L conversion can be compared against programmable thresholds and reported in the STATUS register. Note that the LHR conversion results cannot be used for comparator functionality.

In addition, the INTB signal can be asserted or deasserted when the conversion results increase above a Threshold High or decreases below a Threshold Low registers. In this mode, the LDC1101 essentially behaves as a proximity switch with programmable hysteresis. The threshold HI settings must be programmed to a higher value than the threshold LO registers (for example, if RP_THRESH_LO is set to 0x2000, RP_THRESH_HI should programmed to 0x2001 or higher).

Either Latching and non-latching functions can be reported on INTB/SDO. The INTB signal can report a latching signal or a continuous comparison for each conversion result.

The Threshold setting registers (address 0x06:0x09 and 0x16:0x19) can be changed while the LDC1101 is in active conversion mode. It is recommended to change the register values using an extended SPI transaction as described in SPI Programming, so that the register updates can be completed in a shorter time interval. This functionality enables the LDC1101 to operate as a dynamic tracking switch. LDC1101 output codes can be readout in < 4 μs, and the set of active thresholds can be updated in <6 μs. It is not recommended to update the threshold registers more often than once per conversion interval of the LDC1101 (that is, do not change the threshold register values multiple times in a single conversion interval).

To clear a latched INTB signal, set INTB_MODE = 0x80; it is not necessary for the LDC1101 to be in Sleep mode to clear the latched output; the INTB_MODE can be changed while the LDC1101 is in active mode. After clearing the latched output, re-enabling the INTB_FUNC can be done while in active mode.

space

Figure 56. INTB/SDO Output Value for R_P Comparator with Hysteresis (INTB_FUNC=b00’0010)

Figure 57. INTB/SDO Output for R_P Threshold High (INTB_FUNC=b00’00011)

9.2.1 Design Requirements

Example of an axial measurement implementation using the LDC1101. In this example, the sensor is an inductor constructed of a multi-layer PCB coil in parallel with a C0G grade surface mount capacitor. For this example, a 10 mm diameter Aluminum target of 1mm thickness is moved perpendicular to the plane of the sensor coil.

For this example, the target range of motion is from 1 mm to 3 mm distance from the sensor coil. The position of the target needs to be reported at a sample rate of 3 ksps. The PCB is a 4-layer construction with 0.1 mm (4 mils) minimum feature size.

9.2.2 Detailed Design Procedure

9.2.3 Application Curves

The RCOUNT = 0x00FF curve, which corresponds to a sample rate of 3.87 ksps, will measure the target position with a slightly lower resolution than the RCOUNT = 0x014A used in this example. Over the target movement range of 3 mm, which corresponds to the normalized value of 0.3 on the Axial Measurement graph, the target position can be resolved to 4 µm.

Figure 59. LHR Axial Measurement Resolution vs Normalized Distance for Aluminum Target

Figure 60. LHR Output Code vs Normalized Distance for Aluminum Target