Current, Cable Length, Slew Rate: An Important Relationship

These three equipment-related variables can affect high-frequency vibration measurements.

By Meredith Christman, IMI Sensors, A Division of PCB Piezotronics

Successful collection of high-frequency vibration measurements isn’t as easy as simply choosing the right accelerometer and mounting methodology. A technician also needs to take into account cable length as excessively long cables can have a negative impact on the high-frequency capabilities of a vibration sensor. This is especially important in applications that typically require high-frequency measurements, such as motor/pump bearing faults and gearbox faults.

SIGNAL CONDITIONING

The signal-conditioning process in an IEPE (integrated electronics piezoelectric) sensor starts with the introduction of supply voltage (typically 18 to 28 VDC) into a signal conditioner (integrated or separate). The power then passes through a current-regulating diode to create a constant current power supply (typically 2 to 20 mA). There is an approximate VDC drop across the diode. The remaining DC voltage after the 1-VDC drop across the diode is called excitation voltage. The excitation voltage is then transmitted to the IEPE sensor by cable. The portion of the excitation voltage used to power the sensor’s amplifier is called the bias voltage (typically 8 to 12 VDC). 

The built-in amplifier of a typical industrial IEPE sensor is usually a charge
amplifier, as most industrial vibration sensors use a ceramic sensing element. The sensing element, after being acted upon by a force, produces a high-charge output. The charge collects in the crystal capacitance. The amplifier then converts the high-impedance charge signal into a low-impedance voltage signal, according to the law of electrostatics.

The low-impedance voltage signal is a VAC dynamic signal (typically 0 to 5 VAC for a sensor with a 100-mV/g sensitivity) that rides on top of the bias voltage when being transmitted back to the signal conditioner. When the output signal is received back at the signal conditioner, the DC bias voltage is decoupled from the AC signal voltage to record accurate data. The AC voltage signal that rides on top of the bias voltage swings in the positive and negative direction. In the negative direction, the voltage swing is from a sensor-specific lower limit to the bias voltage. In the positive direction, the voltage swing is from the bias voltage to the excitation voltage. 

The ability of an amplifier to quickly swing the voltage signal from negative to positive is dependent upon its slew rate. Slew rate specifies how significantly an amplifier can change its voltage output in a given period and is typically measured in V/µsec. The required slew rate of an accelerometer amplifier can be calculated with the following formula where f represents the desired frequency response in Hz and V represents the maximum AC output voltage of the sensor in volts.

Slew rate = 2 x π x ƒ x V

As an example, consider the following comparison of the required slew rate of a low-frequency IEPE accelerometer to a high-frequency IEPE accelerometer. This comparison illustrates that frequency response and slew rate can be directly correlated to each other with minimum acceptable slew rate increasing as maximum frequency response increases.

Low-frequency IEPE accelerometer: With a maximum frequency response (±3 dB) of 500 Hz and a maximum voltage output of 5 VAC, the calculation for the required slew rate of the sensor’s amplifier is as follows:

2 x π x 500 x 5 = 0.0157 V/µsec.

High-frequency IEPE accelerometer: With a maximum frequency response (±3 dB) of 30,000 Hz and a maximum voltage output of 5 VAC, the calculation for the required slew rate of the sensor’s amplifier is: 

2 x π x 30,000 x 5 = 0.9428 V/µsec.

Effects of Current and Cable Capacitance on Slew Rate

The low-impedance output signal from an IEPE sensor’s amplifier is typically well suited for transmission over long cable lengths as the signal is generally not susceptible to noise when transmitted long distances. However, as cable runs exceed 100 ft. (30.5 m), signal filtering of high-frequency outputs (greater than 10 kHz) could occur because of cable capacitance.

Cable capacitance is a type of stray, or parasitic, capacitance that is unwanted, yet unavoidable. It occurs when two insulated conductors within a shielded, twisted-pair cable are at different electrical potentials. A polarizing electric field develops across the non-conductive insulator (dielectric) as positive charge collects on one conductor and negative charge collects on the other conductor. Cable capacitance (measured in picofarads, pF) can be affected by distance between the two conductors, type/amount of insulation between the two conductors, or amount of conductor surface area. 

The differential charge between the two conductors allows the storage of energy, i.e., voltage in the electric field, which typically resists a change in voltage. When there’s no change in voltage, there will be no current. Each time the voltage changes, the electric field draws or supplies current to charge or discharge the electric field. If electric-field charging is restricted by a low sensor constant current, the field cannot be charged fast enough to provide adequate current to allow the sensor amplifier to maintain its slew rate. 

The effect of varying current and capacitance are illustrated by the formula below, where i represents current in amps and C represents capacitance in farads. Because of a lower slew rate, the amplifier becomes saturated, and a low-pass filter clips the waveform of signals with a frequency greater than approximately 10 kHz. 

The following example illustrates this formula. It uses a typical low-cost IEPE accelerometer in conjunction with a typical two-conductor cable. The sensor specifications dictate a 10,000-Hz frequency response (±3 dB), ±5 VAC output swing, and a 2 to 20 mA constant current. The cable specifications dictate a capacitance of 36 pF/ft.

As a starting point, the minimum slew rate of the accelerometer is 0.3142 V/µsec. (2 x π x 10,000 x 5) in order for the sensor’s amplifier to be able to handle voltage swings at a 10,000-Hz pace. Table I calculates the actual slew rate of the amplifier, depending on different current/capacitance combinations. (Total current supplied to the IEPE sensor is reduced by 1 mA to compensate for powering the device’s internal electronics.) This table illustrates that current and slew rate have a direct correlation while total cable capacitance and slew rate have an inverse correlation. An increase in supplied constant current can help to offset the large capacitance created by a long cable while a shorter cable or a cable with a lower capacitance specification can offset a low supplied constant current when trying to achieve a particular sensor-frequency response.

MAXIMUM FREQUENCY RESPONSE

As referenced in Table I, the maximum frequency response of an accelerometer with a long cable run is a function of the total cable capacitance and the accelerometer amplifier’s current input. There are two methodologies to determine the maximum frequency signal for a given cable length. 

The first methodology makes use of the following equation.  

In the equation, f_MAX represents the maximum possible frequency response in Hertz, C represents the total cable capacitance in picofarads, V represents the maximum AC output voltage of the sensor and iC represents the constant current excitation. The equation shows that a greater constant current is required as the length of cable, peak voltage output, or maximum frequency increases.

The second methodology uses a nomograph (see Fig. 1, above). A nomograph provides a simple, graphical method for obtaining the expected maximum frequency capability of an IEPE sensor. The sensor maximum output voltage, cable capacitance, and supplied constant current must be known or presumed. Here’s an example: 

• Step 1: 100-ft. cable with a capacitance of 30 pF/ft. = 3,000 pF. Find the appropriate diagonal line.

• Step 2: Sensor maximum output voltage = 5 VAC and constant current = 2 mA. Calculate V/(i_C – 1) = 5/(2 –1) = 5. Find the corresponding value on the vertical axis.

• Step 3: Trace horizontally from the vertical axis value determined in Step 2 to an intersection with the diagonal line determined in Step 1. Then trace down to the horizontal axis. Maximum possible frequency = approximately 10.2 kHz. 

The nomograph doesn’t indicate whether the frequency amplitude response at a point is flat, rising, or falling.

It’s good practice to increase the constant current (if possible) to the sensor (within its maximum limit) so that the frequency determined from the nomograph is approximately 1.5 to 2 times greater than the maximum frequency of interest.

Note that higher current levels will deplete battery-powered signal conditioners at a faster rate. In addition, any current not used by the cable goes directly to power the internal electronics and will create heat. This may cause the sensor to exceed its maximum temperature specification. For this reason, do not supply excessive current over short cable runs or when testing at elevated temperatures.

BOTTOM LINE

A vibration sensor’s supplied constant current, as well as its corresponding cable’s length, can affect its ability to effectively measure high-frequency vibration. As was discussed here, current and slew rate have a direct correlation, while total cable capacitance and slew rate have an inverse correlation. An increase in supplied constant current can help offset the large capacitance created by a long cable. A shorter cable or a cable with a lower capacitance specification can offset a low supplied constant current when trying to achieve a particular sensor frequency response. EP

Meredith Christman is a product manager at IMI Sensors, a division of PCB Piezotronics, Depew, NY. For more information on a variety of vibration monitoring applications and solutions, visit pcb.com/imi-sensors.