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Filtering in Fieldbus

by Analog Services, Inc.

January 15, 1999

Revised March 14, 1999

1.   Introduction

    Foundation Fieldbus is slowly gaining momentum in the process control industry.  Its big advantage over older analog methods is the reduction in control wiring.  The Fieldbus Standard specifies several physical layers, one of which is the "low-power voltage-mode."  This physical layer provides for direct connection to fundamental process devices, and uses Manchester-encoded binary baseband signaling at 31.25 kbits/second.  (See Foundation Fieldbus documents for a description of Manchester encoding.)

    Given that Fieldbus devices must often operate at low power and/or must be intrinsically safe, signal processing circuitry is at a premium and the size of inductors and capacitors is limited.  This leads to the question of what, if any, signal filtering is needed?  Or how simple can a filter be and still be adequate?    Is the implied (in Foundation Fieldbus documents) signal band of 0.25Fr to 1.25Fr wide enough?   And what about signal coupling?  Is the oft-touted advantage of Manchester -- that it doesn't require DC coupling -- a trap for the unwary?  These and other questions are addressed here.  Some simulation results are included to illustrate filter, coupling, and network effects.

2.   Manchester Power Spectral Density

    It's helpful to start by looking at the power spectrum of the Manchester signal.  With no risetime limits the power spectrum is given [1] by

where To = bit time, w = radian frequency.    This is plotted in figure 1.  It's what we get if we Manchester encode a random bit stream and feed the result to a spectrum analyzer and take the average of lots of spectra.  The plot continues to infinite frequency and only the low frequency part is shown.

Figure 1 -- Manchester Power Spectral Density

Just as a square wave has harmonics at 1, 3, 5, etc. times the period, the Manchester signal has harmonic lobes at 1, 3, 5, etc. times the bit rate, starting with the main lobe from 0 Hz to 62.5 kHz.   The main lobe is characterized by a peak near 23.4 kHz, which is midway between 1/To (31.25 kHz) and 1/2To (15.625 kHz).  Another main lobe feature is that it isn't symmetric:  more of the power is found at lower frequencies.  And finally, the power extends down to, but does not include, DC.

    Note that this is the power spectrum for a random bit pattern.   Since Foundation Fieldbus does not require any form of randomization (such as would be provided by a scrambler), actual signals aren't necessarily represented by this spectrum.  The lower frequency components could be more prevalent than implied here.    This has implications for highpass filters applied to the signal, as will be discussed.

    If we remove all of the harmonics of a square wave except for the first, we end up with a sine wave.  If we remove all but the main lobe of the Manchester signal power, we get something like the bottom trace of figure 2.

Figure 2 -- Lowpass Filtered Manchester

It was generated by applying a 256 stage lowpass FIR filter (sample rate = 2 MHz, window = Hamming) with cutoff frequency of 50 kHz to a Manchester-encoded random bit stream.  This filter has a very steep attenuation slope while maintaining linear phase.  Frequencies above the main lobe are attenuated by about 50 dB.  The filtered signal clearly contains the same information as the unfiltered one, except that it is delayed and the sharp corners are removed.  This illustrates that the Manchester signal consists primarily of its main spectral lobe and that this lobe, by itself, is sufficient to represent the signal.

3.   Fieldbus Channel

    The Fieldbus channel is illustrated in figure 3.  The Manchester encoding is done digitally, so that the signal starts out as a square wave with fast edges (upper trace of figure 2).  This is applied to a transmit filter that limits risetime.  Its purpose is to reduce EMI and crosstalk.   This is followed by the network, which consists of the cable segments, terminators, and networked devices.  Finally, a receive filter is used to reject noise and interference.

Figure 3 -- Fieldbus Channel

   Although not explicitly shown, the transmit and receive filters include the coupling to the network.  AC coupling creates a highpass filter that can affect the low frequency end of the main lobe in figure 1.

    Other filters could be envisioned as well.  For example, an equalizer might be added to either the transmitter or receiver.  (If an equalizer is added at the transmitter, then care must be taken that the transmit waveshape requirements in the Fieldbus standard aren't violated.)  Generally there is not a lot of power available to do signal processing, especially in two-wire devices.    Although this will change as time goes on and Fieldbus becomes more highly integrated, the relative simplicity of Manchester and the limited signaling distances in Fieldbus are such that we should be able to get by without anything too exotic.

4.  Receive Lowpass Filter

    Although the receive filter is generally bandpass, it is convenient to split it into highpass and lowpass parts and examine their effects separately.  For now only the lowpass part is considered.  To limit received noise, we want the bandwidth to be low.  But if we chop too much out of the main lobe, we get a distorted signal.  What cut-off frequency should we use and what kind of filter?

    In several places the Fieldbus Standard uses the frequency band of  0.25Fr to 1.25Fr (Fr = bit rate = 31.25 kHz).  This suggests that we should be able to remove the signal power above 1.25Fr = 39.06 kHz.  The Standard also says that power supply interference above 1.25Fr can increase at a rate of 20 dB/decade.  This suggests a single-pole filter with a corner frequency of  39 kHz.  The result of applying this filter is shown in figure 4.  The received waveform is distorted.  But the zero-crossings of the signal, which contain the Manchester information, still look good.  Therefore, this received signal can probably be decoded successfully.

Figure 4 -- 1st Order Lowpass Filter Applied To Manchester Signal

We might want to try to further improve on the noise reduction by using a 2nd order filter.  Figure 5 shows the effects of filtering by 2nd order Butterworth and Bessel filters.  Again there is some distortion.  But either signal could probably be received successfully.  These filters cause the main lobe of the power spectrum to roll off a little more sharply at the high frequency end.

Figure 5 -- 2nd Order Butterworth and Bessel Lowpass Filters
Applied To Manchester Signal

   If 2nd order filters look good, then we might be tempted to assume that a "brickwall" filter must be great.  Well, some are and some aren't.  The filter responses for 8th order Butterworth and Bessel with cutoff at 39 kHz are shown in figure 6.  The Butterworth output now shows noticeable shifts in zero crossings, while the Bessel output is virtually ideal.

Figure 6 -- 8th Order Butterworth and Bessel Lowpass Filters
Applied To Manchester Signal

The plots of figures 4, 5, and 6 were generated using PSPICE [2].   All of the receive filters in these figures are analog.  However, as indicated in figure 2, a digital filter might also be used.  In fact, an FIR filter can be created that is equal to or better than the 8th order Bessel filter (bottom trace of figure 6).

5.    Transmit Risetime

    The transmit filter shapes the transmit signal so that it conforms to Fieldbus requirements.  Shaping can either be done with a linear filter or a nonlinear circuit that shapes the signal in the time domain.  The idea is to give a trapezoidal shape to the transmitted signal.  An example of a nonlinear shaping circuit is that of figure 7.

Figure 7 -- Nonlinear Transmit Shaping Circuit 

     The Fieldbus Standard specifies a maximum slew rate of 0.2 volt/µsec and a maximum risetime (10% to 90%) of 0.25 bit time (8 µsec) for the transmitted signal.  Assume ideal trapezoidal shaping that ramps linearly between levels of -0.5 volt and +0.5 volt (1 volt p-p) and that the ramp time is Tr.   Then the two specifications imply that 5 µsec < Tr < 10 µsec.  It is of interest to determine the effect of this in the frequency domain.   First, note that the ramp is produced by integrating a pulse of duration Tr.  The LaPlace transform of the pulse is P(s) = (1-exp(-sTr))/s.   Integrating this gives us Y(s) = P(s)/(sTr) = (1-exp(-sTr))/(sTr)/s.   However, the input to this process is the step function, whose LaPlace transform is X(s) = 1/s.  Thus, the filter transfer function is H(s) = Y(s)/X(s) = P(s)/Tr = (1-exp(-sTr))/(sTr).   The greatest lowpass effect occurs for maximum Tr = 10 µsec.   The magnitude of the transfer function is given in figure 8 below.

Figure 8 -- Linear Ramp Transfer Function Magnitude

Since this shows roughly 3 dB of attenuation at 40 kHz, it will have some affect on the received signal.  Figure 9 below is a repeat of figure 4 above, but with the transmit waveform shaped before being applied to the receive filters.  The transmit risetime is 10 µsec.  This shows that the combinations of receive and transmit filters still produce relatively good received waveforms.  The upper of the two Manchester frequencies has a slightly lower amplitude as a result of the shaping.

Figure 9 -- 2nd Order Filters Applied to Shaped Manchester Signal

5.  Effect of the Network

    Since the Fieldbus network can vary, it can't be described by a single transfer function.  The transfer function between any two devices depends on what cable is used, the length of each cable segment, device impedances, and where the devices are located.  Although work has been done [3]   to locate and assess worst-case transfer functions in randomly constructed networks, this approach is outside the scope of this presentation.  Instead we will pick a single, typical network configuration and analyze it.  A common construction is to have one device located at one end of the trunk ("home run" in process control jargon) and a cluster of devices at the other end, connected in a "star" arrangement.  Then assume the following:

        1.    All of the devices are identical and appear to the network as a fixed capacitance of 2000 pf.
               This is true whether transmitting or receiving.

        2.    There are 10 devices at the cluster end, each connected through a spur of length 50 meter.

        3.    The trunk length is 500 meter.

        4.    The same type of cable is used throughout and is Fieldbus type A or close to it.

Of course, Fieldbus terminators are also located at each end of the trunk.  The network is illustrated in figure 10.

Figure 10 -- Example Network

We want to find the transfer function between any device at the cluster end and the device at the opposite end.  (The transfer function is the same in either direction.)  This is analyzed in the Appendix for both lumped and distributed models of the cable.  The transfer function that will be used in the following is the distributed model version, given as table A.1 in the Appendix.  

    A PSPICE simulation that combines the transmit shaping with the network transfer function is shown in the lower trace of figure 11.   The simulation was started with the input to the network at 0 volt to avoid putting a starting transient into the response.

Figure 11 -- Combined Transmit Shaping and Network

The lower trace of figure 11 is the voltage seen at the terminals of the receiving device.  The network clearly distorts the waveform more than any filter applied so far.  In particular, there is a slow rolling motion in the average position of the output.  This displaces the zero crossings slightly from their desired locations.   This rolling motion can be easily demonstrated in the lab and is not some artifact of the simulation.

    If all 3 blocks (transmit, network, and receive) of figure 3 are applied and if 2nd order filters are used in the receiver, then the results are as in figure 12.

Trace A = Shaped Transmit
Trace B = Butterworth + Network + Shaped Transmit
Trace C = Bessel + Network + Shaped Transmit

Figure 12 -- Combined Transmit, Network, and Receive Filters

Figure 12 shows that the receive filters have altered the signal only slightly from what it was in the bottom trace of figure 11.  Also, the other filters have now almost obscured any differences between the receiver Butterworth and and receiver Bessel outputs.

   So far we've been concerned mainly with the effects of lowpass filters and removal or alteration of higher frequency components.  The only highpass effects are those contributed by the network.  The next section addresses highpass filters that result from AC coupling.

6.    Effect of Coupling

    Coupling refers to either coupling of the signal onto or off of the network, or to inter-stage coupling within a device. 
When AC coupling is used, we would like to keep the transformer or capacitor doing the coupling as small as possible.  In intrinsically safe devices, especially, there is a lot of pressure to keep inductance and capacitance values low.  But lowering the L or C of the coupling element is synonymous with raising the cutoff frequency of the highpass filter formed by that element.  Figure 1 shows that there is a lot of signal power just above 0 Hz.  In fact the main lobe extends down to, but doesn't include 0 Hz.  If we work with an actual Fieldbus signal instead of a random bit pattern, there may be even more power close to 0 Hz, than is implied by figure 1.  If the cutoff frequency formed by a coupling element is too high, significant distortion can result.  The 0.25Fr = 7.813 kHz limit implied in Fieldbus specifications may be too high.  The following examination of highpass effects will focus primarily on a first order highpass filter, since a coupling element will usually create only one main pole.  One example of two cascaded first order highpass filters is also included, since it is possible that both the transmitting and receiving devices might use equivalent coupling.

    Figure 13 below shows the effect of single-pole highpass filters at 0.25Fr = 7.8 kHz, 0.1Fr = 3.1 kHz, and 0.05Fr = 1.6 kHz applied to the shaped Manchester.

Figure 13 -- 1st Order Highpass Filters Applied to Shaped Manchester

The signal becomes progressively more distorted as the highpass cutoff frequency is raised. 

    In the possible event that highpass filters become cascaded, such as might occur if transmitting and receiving devices use the same coupling, then the effect of cascaded highpass filters is as in figure 14.  For these simulations, the same cutoff frequencies as in figure 13 are used.  That is, for the second trace from the top, both of the cascaded highpass 1st order filters us a cutoff frequency of 0.05Fr.

Figure 14 -- Cascaded First-Order Highpass Filters

The bottom trace of figure 14, which corresponds to 0.25Fr, is heavily distorted.   In fact, the flat tops of the original pulses sag all the way down to zero.   Therefore, 0.25Fr may not be satisfactory in some situations.

    Getting back to figure 13, in all of the highpass outputs there is a slow rolling change in average position of the waveform.  The waveform for 0.25Fr is the worst of the three.  The rolling is similar to that caused by the network but in the opposite direction.  That is, the up-hill part of the waveforms in figure 13 correspond to the down-hill parts of the waveform of figure 11.  When the network effects are added to the highpass filters we get figure 15.

Figure 15 -- Combined Network and 1st Order Highpass Filters
Applied to Shaped Manchester

Here the slow rolling is still present at 0.1Fr and 0.25Fr but not as pronounced as in figure 13.  At 0.05Fr the rolling has all but disappeared.   What seems to have happened is that the highpass filter cancels (equalizes) the effect of the network.  At  0.05Fr = 1.6 kHz the equalization is good.  It gets progressively worse (too much equalization) as the highpass cutoff frequency is raised.  That this happens is also illustrated in the frequency domain in figures 16 and 17.  In figure 16 the magnitudes and their sum are plotted.  The same is done for phase in figure 17.  Only the highpass transfer function for 0.05Fr was used.

Figure 16 -- Transfer Function Magnitudes

Figure 17 -- Transfer Function Phases

The sum in each case represents the transfer function of the combination.  At lower frequencies the two transfer functions cancel each other so that the combined magnitude is nearly flat and phase is nearly zero.

    Looking further at the equalization that occurs between a highpass coupling element and the network, we might ask what part of the network transfer function is being canceled in the equalization.  It seems that the zero caused by the terminators is a candidate (see Appendix), since the RT*CT product corresponds to a frequency of 1.6 kHz, which is 0.05Fr.  It would be interesting to determine whether we can expect this for the majority of networks.  If so, then we might want to build equalization for the terminator into all devices, perhaps in the form of pre-emphasis.   But that's beyond the scope of this presentation.

7.  All Filters Together

    The simulation that produced figure 15 was repeated, except that the 2nd Order Butterworth Lowpass receive filter at 39 kHz was added.  The result is shown in figure 18 below.  The traces have the same significance as in figure 15.   This also looks about the same as figure 15, which indicates that the lowpass receive filter is passing all of the available signal.

Figure 18 -- Highpass, Lowpass, Network, and Shaping Combined

8.  Conclusion

   This has been an examination of the effects of several filters on the Fieldbus Manchester signal.  The filters considered are the receiver lowpass filter, transmit signal shaping, the network, and signal coupling.  Simulations were run to show the effects of the filters in the time domain.  Frequency domain representations of several filters are also presented.  The Manchester power spectrum was plotted and a baseline established for what constitutes the Manchester signal.  It is shown that a highpass filter, such as is produced by AC coupling, tends to cancel network effects in a typical network.  It is also shown that the lower band edge of 0.25Fr implied in Fieldbus specifications should be used with care in designing coupling circuits.  It may not be low enough in some cases.

    Clearly, not everything about Fieldbus can be understood by looking at time domain outputs for one signal pattern.  But these, as well as eye diagrams, are useful in providing a quick assessment of performance and likely sources of trouble.

APPENDIX -- Transfer Function of Network

    The product of frequency and cable length in Fieldbus is high enough that a distributed cable model (transmission line model) should be used in analyses.  However, it is interesting to look at how well a lumped model does in this example.  The lumps consists of each device, each terminator, the trunk, and each spur.  The trunk and spur are modeled as fixed capacitors.  This means that the whole network boils down to a fixed capacitor in parallel with two terminators.   Since a transmitting device is a current source that produces a voltage at the receiving device, we actually compute a transimpedance function instead of a transfer function.  However, this is easily converted to a transfer function by normalizing it to 50 ohm (the combined effect of two terminators).  The resulting transfer function, stated without derivation, is

where CT = terminator capacitance = 1ufd, RT = terminator resistance = 100 ohm, C = combined capacitance of trunk, spurs, and 11 devices = 0.122 ufd.  The common rule of thumb -- that instrument cable has a capacitance of 100 pf/meter -- has been applied.  A plot of the magnitude and phase of the transfer function is given in figure A.1.

Figure A.1 -- Lumped Element Transfer Function of Example Network

    For the distributed analysis, cable data is only available in the form of tables [4] of transmission line parameters versus frequency, which means we can't find an analytical form for the transfer function.  Fortunately, however, PSPICE allows input in the form of tables. 

    The steps involved (for each frequency) are:

            1.     Compute the reflection coefficient for the spur, loaded by the device.

            2.     Using the result of step 1, compute the driving point impedance for the spur.

            3.     Using the result of step 2, compute the load impedance seen at the cluster
                    end of the trunk.  This consists of the 10 spurs and one terminator.

            4.     Using the result of step 3, compute the reflection coefficient for the trunk.

            5.     Using the result of step 4, compute the driving point impedance of the trunk.

            6.     Combine the result of step 5 with the impedances of one device and one
                   terminator located at the non-cluster end of the trunk.

            7.     Calculate the driving voltage at the non-cluster end of the trunk by
                   applying a current source of 0.02 amp to the result of step 6.  Notice
                    that if the impedance were real and equal to 50 ohm, the output would
                    be 1 volt.

            8.     Calculate the transfer function of the trunk and multiply by the driving
                    voltage to arrive at the voltage at the cluster end of the trunk.

            9.     Using the voltage from step 8, multiply by the transfer function of a spur to
                    get the voltage at any receiving device.

The latter voltage is the desired transfer function.  It is actually an array of complex voltages -- one for each frequency.  The actual calculations are omitted here and only the results are given in table A.1.

Table A.1 -- Network Transfer Function

The network transfer function magnitude and phase are plotted in figure A.2.  The result is similar to the lumped model transfer function (figure A.1).  As might be expected, agreement becomes worse at higher frequencies.

Figure A.2 -- Transfer Function of Example Network

REFERENCES

1.   Lathi, B.P., Modern Digital and Analog Communication Systems, Holt, Rinehart, and Winston, 1983, chapter 3.

2.   PSPICE, Release 8, Microsim Corporation, 20 Fairbanks, Irvine, CA 92618.

3.  Rosemount Inc. report entitled "Simulation of H1 Networks,"  no date given, Rosemount Inc. 12001 Technology Drive, Eden Prairie, MN.

4.   Anderson, S.D., "Cable Characteristics for Fieldbus," IEEE IMTC/92.

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