While it is often acceptable to think of wire as an ideal conductor that simply gets a signal from point A to point B, this is rarely the case for long cable runs. In the real world, appreciable lengths of field wiring will introduce constraints on the signals produced by the sensor and then routed to the monitoring channel. In this article, we explore one such length constraint: that imposed by hazardous area limitations1Refer also to vibro-meter application note “The Use of vibro-meter Front-Ends in Potentially Explosive Atmospheres: Ex certification and its implications” (document 660-040-002-201A / 08.03.2010(coming soon)).. In a companion article2“Four effects you can’t ignore in field wiring” (coming soon). and corresponding application note3“Considerations regarding the influence of cable length on frequency attenuation in vibro-meter sensor measuring chains” vibro-meter application note (document 660-040-001-201A / 04.15.2022)., the other primary length constraint is explored: frequency response limitations. Although the examples in this article use a proximity measurement chain, the principles discussed are universally applicable to any type of sensor involving substantial lengths of field wiring.
In an ideal world, the wire connecting a sensor to its associated monitoring system would look as depicted at the top of Figure 1. In the real world, however, it must be modeled as depicted at the bottom of Figure 1 where there is distributed capacitance, inductance, and resistance. These values are typically expressed on a per-meter or per-kilometer basis when SI units are used. In this article, we will refer interchangeably to this field wiring as “transmission cable” when necessary to distinguish it from other signal cables such as the coaxial cable used in proximity measurement chains and acceleration measurement chains. In Figure 1, the sensing element, its signal conditioner, and the special-purpose interconnection cable between the two are thus lumped into a single entity that we have denoted “sensor”. The transmission cable then becomes the wiring that connects this sensor to its corresponding monitoring system.
Figure 1: Ideal field wiring (top) has no resistance, inductance, or capacitance. Real field wiring (bottom) exhibits distributed resistance, inductance, and capacitance as shown.
As an example of routinely employed transmission cable, consider vibro-meter K310. It consists of a triad (PWR, SIG, COM), a braided shield for the overall triad, and a polyurethane outer jacket. It is often used for powered sensors such as proximity probe measurement chains and Hall-effect sensors. An excerpt from the datasheet is shown in Figure 2.
Figure 2: The datasheets for our cables provide the capacitance, resistance, and inductance values needed for both hazardous area and frequency response calculations.
When determining the allowable maximum length of cable in a hazardous area, a key parameter to determine is the effective capacitance (Ccable). A comprehensive treatment of how to determine Ccable for an arbitrary number of conductors, shields, and all possible wiring configurations is rather complex and well beyond the scope of this article. However, a number of excellent references on this topic exist for the interested reader4As one example, the engineering note “How to read catalog data – capacitance” published by Mogami (now a division of Marshall Electronics) contains an excellent discussion of the equations used and their derivations. The note is archived at www.mogami.com (retrieved Apr 5, 2022).,5Another example can be found in the discussion “What is conductor to conductor to shield capacitance” at the Electrical Engineering StackExchange community (www.electronics.stackexchange.com).. It is sufficient here merely to show what values to use by looking at a manufacturer’s datasheet rather than a detailed discussion of how those values are determined.
The first question one might ask when looking at a datasheet from vibro-meter or any other supplier of cable is why Ccable is not listed directly – and instead several other values are typically given, such as core-to-core capacitance. The reason is simple: a value of Ccable is application dependent and is affected by not only the cable geometry and materials of construction, but also how the user is going to use the conductors and connect the shield. For example, for vibration applications, it is very typical for the user to connect the COM conductor to the shield at one end6It is not connected at both ends because this would lead to a ground loop. but to otherwise use all three conductors for separate purposes. It is also typical to use a so-called “common-mode” (COM, SIG) signal transmission scheme rather than differential mode (+, -).
Because application-specific values in a datasheet will only be helpful to some users and not all users, it is thus typical for manufacturers to present capacitance values that are designed to be independent of the application. The user must therefore select not only the correct values, but possibly perform additional calculations to determine the effective capacitance (Ccable) for the application. Table 1 below shows the capacitance data one will typically encounter when looking at a cable manufacturer’s datasheet:
For both hazardous area calculations and general frequency response calculations, the ideal value to use is Cc-o+s. When this value is provided, no additional calculations are needed to determine the effective capacitance. Thus, referring to the vibro-meter datasheet of Figure 2, we would use a value of 100 pF/m for Ccable when using K310. In contrast, when looking at the Belden data of Figure 3, we would use a value of 140 pF/m for Ccable and when looking at the AlphaWire data of Figure 3, we would use a value of 289 pF/m (88 pF/ft) for Ccable.7The part numbers for the Belden and AlphaWire cables corresponding to the properties shown in Figure 3 are intentionally omitted. They were selected simply because they are representative of the types of data provided – not because they are necessarily suitable cables for a hazardous area installation.
However, in the event that this value is not directly provided by the cable manufacturer, Ccable can be calculated from other parameters as follows:
(i) Ccable= 2 ∗ Cc−c+ Cc−s (triad cable)
For 2-wire (twisted pair) cable, the total capacitance can be calculated as follows:
(ii) Ccable= Cc−c+ Cc−s (twisted pair cable)
Note here that Cc−s(conductor-to-shield) is used – not Call-s (conductors-to-shield). Because vibro-meter provides Cc-o+s in our datasheets, additional calculations to determine Ccable are not needed in most cases. As such, we will not provide examples of computations using Equations (i) or (ii); they are both simple and straightforward to use when needed.
Figure 3: The datasheets of other cable manufacturers also typically provide capacitance, resistance, and sometimes) inductance values, but may use different nomenclature. If in doubt, consult the cable manufacturer.
Resistance is rarely as potentially confusing to interpret from a datasheet as capacitance can be. As one would expect, the conductors in most instrumentation wiring are typically identical and made of copper, while the shield may be foil, braided, or some other construction and using a material other than copper. Consequently, the conductors will all typically have the same resistance while the shield will usually carry a different value.
While most cable manufacturers publish their distributed resistance and capacitance values in datasheets, the same may not be true of inductance. For example, in Figure 3, notice that Belden does not provide an inductance value. Should this occur for the proposed cable, contact the manufacturer. In contrast, notice that vibro-meter cable datasheets always contain this information and that the datasheet selected from AlphaWire in Figure 3 also contains this information.
One reason that manufacturers may not routinely include this in their datasheets is that the values are typically quite small8The value is frequently around 1 μH/m or less, but may vary; consult the manufacturer. and such small values are frequently not of concern for frequency response calculations. However, because both capacitance and inductance can store energy, the inductance may become important for hazardous area applications and should always be determined to ensure it does not exceed allowable values. Indeed, in some hazardous area applications the cable inductance may become the limiting factor rather than the cable capacitance. Consult the cable manufacturer if the distributed inductance information is not available in their datasheets.
The resistance, inductance, and capacitance inherent in the cable used for field wiring leads to two constraints. One (frequency response) is of concern for all installations while the other (energy storage) is of concern only for hazardous area installations where intrinsic safety will be used as the means of protection. In instances where length constraints exist due to both energy storage and frequency response, perform the necessary calculations for each and then adhere to the more restrictive of the two.
Both the capacitance and inductance in a circuit represent the ability to store energy. The basis of intrinsically safe (I.S.) installations is to limit this energy so that even if a spark were to occur (such as inadvertently cutting a wire and shorting two or more conductors), the spark would not contain sufficient energy to ignite the flammable atmosphere. I.S. installations thus do not prevent sparking – they simply limit the available spark energy such that gas or dust ignition cannot occur. Consequently, the total amount of inductance and capacitance in the circuit (field wiring plus sensing apparatus) becomes a constraint in installations where the sensing apparatus is located in a hazardous (i.e., flammable atmosphere) area. In the example later in this article, we show how to identify these parameters and compute the allowable length using actual vibro-meter products and approvals certificates. It is worth noting that the safe transmission cable length calculated in this manner can be shorter than the length that preserves the desired frequency response (see #2 below), or it could be longer. Therefore, when defining a measuring chain for a hazardous environment, the cable length should always be calculated according to both criteria – frequency response and allowable hazardous area capacitance – and the more restrictive of the two resulting length constraints selected. It is not the intent of this article to discuss all of the many nuances and details of hazardous area calculations, and the details will indeed vary based on the particular region of the world and corresponding approvals agency. Numerous excellent references exist for the interested reader9“A User’s Guide to Intrinsic Safety” MTL Application Note AN9003 (Aug 2009).,10Type of Protection: Intrinsic Safety – Part of the Pepperl+Fuchs Explosion Protection Compendium” Pepperl+Fuchs Application Note (Oct 2019). Part No. 70113819 10/19 00.
When the inductance is removed from the bottom of Figure 1, we are left with a simple low-pass filter (single-pole R-C). The cable will thus attenuate high frequencies while passing low frequencies and must be selected such that the necessary frequency content from the sensor can be transmitted to the monitoring module with little or no attenuation. These considerations pertain to all applications – whether in a hazardous area or not. Particular emphasis is placed on the importance of frequency response12The pulse train signal generated by speed and phase measurements means that the slew rate is also very important in preserving signal integrity and is often the largest contributor to distortion of the original waveform. However, the auto-triggering algorithms employed in vibro-meter monitoring systems are able to compensate for considerable degradation of the original waveform, allowing accurate triggering from less-than-perfect waveforms. in speed and phase measurements given the pulse-like (rectangular waveform) shape of most speed signals.
Most modern approvals for industrial instruments in hazardous areas use the concept of intrinsic safety and entity parameters. Entity parameters describe the limitations on voltage, current, power, capacitance, and inductance of the approved device (“intrinsically safe device”) as well as the limitations on the other devices (“associated devices”) that may be safely connected to it.
It is helpful to think in terms of an intrinsically safe circuit as consisting of three components as shown in Figure 4: The field device (sensor system), the field wiring (transmission cable), and the safety device (Zener barrier or galvanic isolator).
Figure 4: An intrinsically safe circuit consists of the field device, the field wiring, and the safety device. The role of the safety device is to limit the available energy such that a spark in the field wiring or field device will not be able to ignite the flammable atmosphere, nor could enough energy be supplied to create a temperature in the field wiring or field device that could ignite the flammable atmosphere.
Field devices can be further classified as simple devices or non-simple devices. A simple device is one that cannot generate or store more than 20μJ, 25mW, 1.2V, or 100mA. Simple devices do not have entity parameters. However, most vibro-meter field devices (sensors) have at least one component within the measurement chain that is considered a non-simple device and will thus have entity parameters. Examples include the vibro-meter IQS450, IQS900, and IPC707 signal conditioners.
The safety device most commonly used with vibro-meter installations is our GSI 12713The GSI 127 is approved for use in Zone 2 / Div 2 areas, meaning it does not strictly need to be installed in a truly non-hazardous location. The “safe” area of Figure 4 may thus be either a non-hazardous area or a Zone 2 / Div 2 area. This gives the GSI 127 additional installation flexibility while still allowing the connected field device and field wiring to be located in Zones 0/1 or Div 1., a galvanic isolator. However, for customers that prefer passive or active Zener barriers, such devices can often be used in lieu of the GSI 127 and the user will refer to the approval certificates for the specific safety device chosen as well as those of the connected field device
Each of the items in Figure 4 can be described in terms of entity parameters.
Associated Apparatus: These devices are located in the safe area and act as the barrier or interface between the safe area and the hazardous area.
14The nomenclature used may vary depending on the particular approval agency.
Intrinsically Safe Apparatus: These are the non-simple devices located in the hazardous area and connected to the associated apparatus.
3“Considerations regarding the influence of cable length on frequency attenuation in vibro-meter sensor measuring chains” vibro-meter application note (document 660-040-001-201A / 04.15.2022.
For example, when looking at the approvals it is important to note that the maximum capacitance and inductance connected to associated apparatus are contributed by both the field device and the field wiring (transmission cable). In other words, if Ca is the maximum capacitance that can be connected to a safety device, then the connected capacitance will consist of both the capacitance in the field device (Ci) and in the field wiring (Ccable). Consequently, in equation form, all of the following relationships must be satisfied to comply with the conditions in the hazardous area certification:
1) Ca ≥ Ci + Ccable
2) La ≥ Li + Lcable
3) Ui ≥ Uo
4) Ii ≥ Io
5) Pi ≥ Po
The distributed capacitance and inductance will be available from the cable manufacturer while the other values will be available from the manufacturer of the device(s) and typically contained within their approval certificates and associated drawings. Armed with this information, it then becomes straightforward to solve for the maximum allowable cable length.
The easiest way to reinforce understanding of the concepts discussed thus far is by means of a concrete example using specific vibro-meter devices and a specific transmission cable. The concepts can then be applied in analogous fashion to other field devices (whether used for speed measurements or other measurements), other safety devices (whether galvanic isolators or passive Zener barriers), and other cable manufacturers.
For this example, we will consider the maximum cable length permitted in an ATEX Zone 0/1 hazardous area using an intrinsically safe circuit. The details used for this example are summarized in Table 4.
Referring to the five equations provided earlier, we can see that equations 3, 4, and 5 are independent of cable length and are satisfied. Equations 1 and 2 will depend on cable length for the total amount of capacitance and inductance, respectively. The equations then become as follows:
1) Ca ≥ Ci + Ccable ➔ Ca - Ci = Ccable ➔ 95 nF – 4.4 nF = 90.6 nF = Ccable
Ccable = DC (distributed capacitance) x CLmax (max cable length)
CLmax = Ccable / DC = (90.6 nF) x (1000 pF/nF) / (100 pF/m) = 906 meters
2) La ≥ Li + Lcable ➔ La - Li = Lcable ➔ 5 mH – 9.92 μH = 4.99 mH = Lcable
Lcable = DL (distributed inductance) x CL (cable length)
CL = Lcable / DL = (4.99 mH) x (1000 μH / mH) / (0.9 μH/m) = 5544 meters
As this example shows, the inductance is not the limiting factor on cable length for hazardous area concerns. Instead, it is the capacitance. Here, we can connect no more than 906 meters of K310 transmission cable if we are to remain within the allowable maximum capacitance supported by the GSI 127 for ATEX approvals. In contrast, more than 5.5 km of cable could be run before the maximum allowable inductance was exceeded.
Let’s assume, however, that our application requires us to run a full 1 km of cable. There are several options available:
Figure 5: The GSI 127 can be located between the IQS900 and the monitor module. This would be one way to observe the 906 m maximum length limitation for cable capacitance in the Zone 0/1 hazardous area if the monitor module is located 1 km from the sensor.
In this article, we have explained how the maximum length of transmission cable is constrained by two factors: frequency response and stored energy. Stored energy is only of importance in hazardous area installations using intrinsic safety. This energy can be stored in the form of capacitance or inductance, and both should be examined as part of the assessment process. We also showed that when extremely long wiring runs are required, a cable with lower capacitance per unit length can be selected, or the safety device (in this case, the GSI 127) could be placed at some intermediate location that is within the maximum length of I.S. cable and then running non-I.S. cable the remaining distance to the monitoring module. The cable itself (in this case, vibro-meter K310) is the same, but on one end of the GSI 127 it is intrinsically safe and within the total capacitance constraints, while on the other end of the GSI 127 we are no longer constrained by capacitance and can continue our cable run to the required 1km length – or even longer lengths as long as the additional length can preserve the required frequency response needed by the application.
We also discovered that although the topics addressed in this article are pertinent to all sensor types, the signal degradation caused by long lengths of field wiring can often be better tolerated in speed/phase signals than in other signal types due to sophisticated auto-triggering algorithms embedded in vibro-meter monitoring systems.
Lastly, we directed the reader to a newly revised Application Note3“Considerations regarding the influence of cable length on frequency attenuation in vibro-meter sensor measuring chains” vibro-meter application note (document 660-040-001-201A / 04.15.2022 that is highly recommended for those that want to explore the topic of frequency response and field wiring length in greater depth. It contains equations and example calculations to help reinforce the concepts involved. It discusses the aforementioned auto-triggering algorithms for speed signals. And, it explores in much greater depth the option for a current-mode output rather than voltage-mode output on speed and vibration signals. This capability is unique to vibro-meter and provides numerous advantages, including support for longer cable lengths than with a voltage-mode output.