The Magic Loop – Part 2

Techniques of using magnetic field loops

by Dr. Min Zhang, the EMC Consultant

Mach One Design

Types and Constructions

Round shape or square shape? 

The shapes of a magnetic field loop don’t matter that much. However, it is highly recommended that square shaped magnetic field loops should be used for EMC troubleshooting purposes. The reason is simple, as demonstrated in Figure 4, square shaped magnetic field loops have the advantages of being easy to couple to the subject under test. The mutual inductance of a square shaped loop is also relatively easier to quantify compared with that of a round shaped loop. 

Figure 4 Square shaped vs round shaped magnetic field loop

Shielded or unshielded?

The debate of shielded or unshielded magnetic field loops can be found in [2]. According to [2], unshielded loops work well as the shielded types in most applications. They are widely used for noise injection purposes during the pre-compliance immunity test.  

Construction of a simple unshielded magnetic field loop and instructions of making shielded types can be found in [2]. Compared with unshielded loops, making a shielded loop takes much longer time and cost more. The trick of making shielded magnetic field loops depend on the semi-rigid coaxial cable. The best cables for making shielded magnetic field loops are 

  1. Mini-circuits Hand-flex Interconnect, 0.086’’ centre diameter coaxial cables for making a 8 cm magnetic field loop.   
  2. Mini-circuits Hand-flex Interconnect, 0.047’’ centre diameter coaxial cable for making a 4 cm magnetic field loop. A larger diameter such as the 0.086’’ cable cannot be bent to form a small loop such as the 4 cm loop. 
Figure 5 Using a mini-circuits hand-flex coaxial cable to make a 4 cm shieled magnetic field loop 

The Magic Loop – Part 1

Techniques of using magnetic field loops

by Dr. Min Zhang, the EMC Consultant

Mach One Design

Theory

The simplest form of a transformer is a pair of wires placed in close proximity. When a changing current I1 goes through conductor 1, there is voltage induced on conductor 2 (assuming conductor 2 is open circuit). The induced voltage is defined as 

V2 = M dI1/dt,

where M is the mutual inductance between the two conductors. 

Figure 1Two conductors as a 1:1 transformer

Therefore, a square magnetic field loop shown in Figure 2 is ideal to measure the induced voltage on one side of the loop, which is proportional to the rate of change of flux generated by rapidly changing current in the wire under test. Such a loop is called magnetic field loop, or “H-field loop”. But it is more accurate to be called a “dΦ/dt” loop. 

Figure 2 An unshielded square magnetic field loop placed alongside a wire

It is important to emphasize here that the output of the square magnetic field loop is a voltage measurement (assuming the other end of the coaxial cable is connected to either a spectrum analyzer or an oscilloscope with a 50-ohm impedance). 

Since the mutual inductance M is less than the inductance of either conductor, the output of a magnetic field loop is a lower bound for the voltage per unit length across the inductance of a current carrying conductor [1]. 

Note, a few assumptions are needed to make the sense of a magnetic field loop. 

  1. The circumference of the loop is significantly less than ½ wavelength at the frequency of interest. This is because the loop could self-resonate. For instance, for a 8 cm long loop, the self-resonant frequency is about 2GHz. This means the loop can be useful up to at least 1 GHz. 
  2. The opposite side of the loop is far enough away so the induced voltage on the far/opposite side of the loop is neglected (see Figure 2).  
  3. The perpendicular sides of the loop do not induce voltages (see Figure 2).
  4. The parasitic capacitance between the magnetic field loop and the wire is ignored. 

According to [1], a magnetic field loop can be modelled as shown in Figure 3. In this case, a 8 cm magnetic field loop is simulated (with circa 2 cm long conductors on each side). The 10 nH inductance value is the mutual inductance M. The 70 nH is the self-inductance of the loop. The 50 ohm impedance (of either a spectrum analyzer, or an oscilloscope with 50 ohm impedance) forms an L-C filter with the inductance of the loop. This causes the cut-off frequency shown in the frequency response.   

Figure 3 Voltage and current responses of a magnetic field loop

As it can be seen, the voltage response of a magnetic field loop is flat until the cut-off frequency (in this case, around 100 MHz). Above this frequency, the sensitivity of the loop starts to drop at a rate of -20dB/dec. This means the loop is useful for voltage measurement till at least 100 MHz. 

The current response of the magnetic field loop (shown in green in Figure 3) means that a magnetic field loop can be used to measure (or to put it more precisely, estimate) high frequency current (whose frequency contents extend beyond the cut off frequency of the magnetic field loop). However, in general, this is not a preferred approach. This is because the mutual and self inductance of a loop is difficult to quantify (really depends on the loop construction and how one places the loop on the PCB, or next to a wire). Thus, the transfer impedance (the ratio between measured voltage to the current) of a magnetic field loop is almost impossible to calculate. 

Separate Common-mode and Differential-mode Signals

By Dr. Min Zhang, the EMC Consultant

Mach One Design Ltd

PDF download link

There are two common ways of separating common-mode and differential-mode noise. One is the voltage method; the other is the current method. 

When using voltage method, a LISN-Mate is often used [1] [2] [3]. When using current method, an RF current probe can be configured to measure either common-mode or differential-mode noise depending on the wiring configuration. 

I have demonstrated how to set up the test using both methods, see https://youtu.be/0uCXs602_6M. The set-up can be found in Figure 1. This article is a follow-up, which discusses the test results and tries to make sense of it. 

Figure 1  Test set-up; (a) LISN-MATE common-mode measurement (b) current probe common-mode measurement (c) LISN-MATE differential-mode measurement (d) current probe differential-mode measurement (insulation form removed to show the configuration)

We used a buck converter as the DUT and set up the test. The LISN-MATE test result can be found in Figure2. 

Figure 2 LISN-MATE results

We then used the current probe method and compared the results with the LISN-mate result. Because current probe measures the current, we need to find a way of converting the results into voltage. This is done in the control software EMCView, where two settings are very important. 

Figure 3 The Tekbox EMCview can be set up to convert current reading to voltage

The first setting is the Lisn/Att Cor where I selected the transfer impedance file of the current probe I used. The current probe manufacturers should always provide you with the transfer impedance file of the probe you purchase. This file converts the voltage reading of a spectrum analyser to current reading (dBμV to dBμA, as dBμA=dBμV-dBΩ, where dBΩ is the transfer impedance). 

The second setting is that I added a 28 dB attenuation compensation. And the reason is:

Both LISNs used for the current probe set-up are terminated with 50Ω resistors. This is important. When I measured IDM using a current probe, I have measured 2×IDM due to the wiring configuration of the current probe on the cable, so I would need to divide the value by 2, or subtract 6dB on the output. The differential voltage is measured on a 50Ω in the LISN voltage set-up, this means I will then need to add 34dBΩ (50Ω) to give me the DM voltage. That means 28dB compensation file in EMC view. 

When I measured ICM using a current probe, I also measured 2×ICM according to the picture below, so I also need to subtract 6dB on the output, then add 34dBΩ (50Ω) to give me the CM voltage reading. That means, again, 28dB compensation file in the EMC view.

Figure 4 The DM and CM voltage relationship to current [4]

The comparison between voltage (LISN-MATE) and current measurement are shown in Figure 5 and Figure 6. Note that in order to see the difference more clearly, we turned off the attenuator in the current probe measurement, this results in a lower noise floor. 

On the differential-mode noise (Figure 5), from 150kHz to 30MHz both methods are amazingly close (error difference is within 2-3 dB), from 40-100 MHz, the LISN-MATE gives 4-6dB higher reading. But from 30MHz upwards, common-mode noise starts to dominate, there will be CM to DM conversion in the system set-up, so I expected measurement difference between the two in this frequency range.

On the common-mode noise (Figure 6), it is the low frequency range (150kHz to 30MHz) that shows 6-10dB measurement difference. From 30MHz onwards, the noise is predominantly common-mode, therefore the measurement difference in this frequency range is not big. 

Figure 5 Differential-mode noise
Figure 6 Common-mode noise

In summary, both the LISN-MATE and current probe methods can separate differential and common-mode noise well. The differential-mode noise is dominant in the lower frequency range (sub 30MHz), so I tend to trust the differential mode noise results in this region. From 30MHz, noise is predominantly common-mode, so in this frequency range, I tend to trust the common-mode noise results.  

Reference

[1] H. W. Ott, Electromagnetic Compatibility Engineering, New Jersey: Wiley, 2009. 
[2] Tekbox, “LISN-MATE,” [Online]. Available: https://www.tekbox.com/product/TBLM1_LISN_Mate_Manual.pdf.
[3] K. Wyatt, “Review: Tekbox LISN Mate is valuable for evaluating filter circuits,” [Online]. Available: https://www.edn.com/review-tekbox-lisn-mate-is-valuable-for-evaluating-filter-circuits/.
[4] T. Hegarty, “An Engineer’s Guide to Low EMI in DC/DC Regulators,” [Online]. Available: https://www.ti.com/lit/eb/slyy208/slyy208.pdf?ts=1629121242544&ref_url=https%3A%2F%2Fwww.ti.com%2Fproduct%2FLM5155.

Some details regarding to conducted emission test set-up

By Dr. Min Zhang, the EMC Consultant

Mach One Design Ltd

PDF download

I wrote in the past about how to set up conducted emission pre-compliance EMC test and made videos demonstrations https://youtu.be/KHxbk4eToXs . There are some details regarding to the test set-up. Here I summarised it below:

  1. 50Ω terminations. If two LISNs are used(as what a typical automotive application would be), make sure that one of the unmeasured LISNs (if you are measuring the 12V line, then it is the 0V line LISN) is terminated with a 50Ω resistor. Failing to do so will result in big test error. See below:
Figure 1  Error results caused by the 50 Ω termination resistor missing from the LISN

2. How important is the 1μF input capacitor to the LISN?

In some of the commercially built LISNs, there’s a switch for switching the 1μF input capacitor, shown in Figure 2. The 1μF input capacitor is used in the conducted emission test, but you have to switch it off if you are doing any kind of transient test, because the capacitor could potentially short the transient.

The Texbox LISNs I use don’t have the 1μF input capacitor built in, so it is recommended that the users should fit it themselves, as shown in Figure 3 & Figure 4 [1].

Figure 2 Schematic circuit diagram of NNBM 8124
Figure 3 Schematic of Tekbox TBOH01 and its recommended external capacitor [1]
Figure 4 Schematic of Tekbox TBOH01 and its recommended external capacitor [1]

So how important is this 1μF input capacitor for the conducted emission measurement? We consulted Tekbox and here’s what they replied:


Looking at the impedance specification of a 5μH LISN – actually I pasted the DO160 spec, because it gives a clearer picture, as it is specified down to 10kHz:

Figure 5 LISN impedance characterisitics 

From approximately 3 MHz to 110 MHz, the 5μH inductor has a high impedance and the impedance of the LISN is dominated by the 50 Ohm load impedance at the RF terminal and the capacitor is not relevant. Below 3 MHz, the impedance of the 5μH inductor decreases and in combination with the low impedance of the capacitor, the overall impedance decreases. At approximately 20kHz, the inductor impedance becomes close to zero and the capacitor starts to dominate, as its impedance increases with decreasing frequency.

I made impedance measurements with the 1μF capacitor removed. At approximately 1MHz, the impedance crosses the red limit line and you would start measuring higher spurious levels, compared to what you would measure with the 1μF capacitor.

Consequently, with or without capacitor, above 1 MHz there is no effect on the measurement result. Below 1 MHz, the measured spurious levels will be higher, compared to the correct set up. However, it will never be a lot, as there are always capacitors in the power supply – at 150 kHz it may be approximately 2~3 dB higher, if you have 1-to-2-meter supply cable length.

Interestingly, a customer came up with a similar question, as our wiring diagram seems weird at the first look:

Figure 5 LISN set up for conducted emission [1]

Above 150 kHz, the impedance of the capacitor is pretty low. Consequently, I simply replaced it by a short connection. For the LISN impedance from 150kHz to 110MHz is does not make a difference, whether you have a capacitor or a short at the source side of the LISN. For DO160 a short would be ok as well, as there is no minimum limit for the impedance below 100 kHz. However, the 1μF capacitor needs to be replaced by a 10μF capacitor, in order to avoid crossing the upper impedance limit at very low frequencies.

Replacing the capacitor by a short is also not a violation of CISPR 16, as the standard requires the LISN impedance to be within Limits with both shorted or open source terminals.

In practice, the measurement results of a set up without the 1μF are most likely fine, as long as the supply wires are short. The 5μH inductor mimics a 5m cable harness, typical for the maximum cable length you would have between car battery and an electronic device in a car. In a set-up that sees a 25 cm cable length and have the output capacitors of your power supply providing the low impedance at the source side of the inductor.”

Reference

[1] M. Mayerhofer, “Conducted emission measurement using the Tekbox 5μH LISN TBOH01,” [Online]. Available: https://www.tekbox.com/product/AN_Conducted_Noise_Measurement_Tek boxLISN_TBOH01_EMCview.pdf.

Homemade Bulk Current Injection Probe, Improved

By Dr. Min Zhang, the EMC Consultant

Mach One Design Ltd

You can download the PDF version of this article in the link below

Background

I have made a current injection probe for a quick troubleshooting job in the past, see [1], I also made a Youtube video demonstrating the test set-up, which can be found in https://youtu.be/JxfNYCbv79o .

The current injection probe was made as a quick-and-dirty approach and I never got a chance of testing the performance of it nor optimizing it. However, due to a question asked by an engineer about the wire size of the probe, also a recent article published by Arnie Nielsen [2], I decided to have a closer look at the injection probe. The aim is simple, to test the performance of it and improve it if possible.

The key point made in Arnie’s article is that by having a multiple-wire configuration, the VSWR is getting large and the performance of the injection probe starts getting detrimental. I believe this is true. In fact, I contacted Arnie and he kindly shared with me the paper his probe was based on [3]. A quick check on those properly made commercial products also indicates a ratio of 1:1. So the best approach we can take is to have a direct comparison test between the single-wire and multi-wire configuration.

The build

Construction of a single-turn winding is easy, here we used a copper that is about 1.5 cm wide and 12 cm long. Be careful about the sharp edges of the copper when making the winding. The best is to use Kapton tape to wrap around the copper, this provides both protection against the sharp edge and insulation. After that, wind the copper around the core (same core as my previous build, i.e. 28A5131-0A2) and solder a BNC connector to the single turn winding, see Figure 1.

Figure 1 Build a single-wire configuration of a current injection probe

A test jig was also built based on [2], as it can be seen from Figure 2. The two current probes under test were shown in Figure 3.

Figure 2 A test jig was built to test the performance of the current probe, a 3dB attenuator was used between the power amplifier to prevent mismatch, a 30dB attenuator was used before the spectrum analyser RF input to prevent excessive high-level of signals damaging the RF front of the spectrum analyser
Figure 3 Two probes are under test, left – multi-wire configuration, right – single-wire configuration

Test set-up

We will need two RF amplifiers to test the frequency range from 100kHz up to 1 GHz. To make things easy, I was using Texbox EMCView software to automatically generate the reference signal (in which frequency, amplitude and dwell time can be set). Two spectrum analysers were used in this case, one is to serve as an RF signal generator (by using its tracking generator output). The other one is used to monitor the injected current on the test jig.

Figure 4 Left, two RF amplifiers from Tekbox covers the range from 100kHz to 1GHz; Right, the test set-up

Performance Comparison

In the frequency range between 100kHz and 10MHz, single-turn winding configuration generates about 12dB more current compared with multi-turn configuration, but at the beginning of the spectrum (from 100kHz to 700kHz), the performance of the single-turn winding is not that good. Note that we measured the injected current in the test jig. The reading needs to be post analysed to get the true injected current level, but for a comparison study, we just look at the dB difference between the two probes.

 Figure 5 Comparison between single-turn winding and multi-turn winding injection probe, 100kHz – 10MHz

In the frequency range of 10MHz and 100MHz, single-turn injection probe performs much better, its output is flat and achieves higher level of injection current across the full spectrum, while the multi-turn injection probe’s performance starts dropping after 50MHz.

Figure 6 Comparison between single-turn winding and multi-turn winding injection probe, 10MHz – 100MHz

In the frequency range between 100MHz and 500MHz, often a frequency range that automotive companies care about the most, one can see the single-turn winding configuration performs much better (flat and maintains a high level of current level).

Figure 7 Comparison between single-turn winding and multi-turn winding injection probe, 100MHz – 500MHz

In the frequency range of 500MHz – 1GHz, the performance comparison is shown below:

Figure 8 Comparison between single-turn winding and multi-turn winding injection probe, 500MHz – 1GHz

Injected current level

So what’s the injected current level that is achieved using a single-turn winding configuration? Assuming 100dBμV reading from the test set-up, the 100dBμV was measured on the spectrum analyser (which has a 50Ω input impedance). We had a 30dB attenuator before the reading, so the true voltage reading is 130dBμV. Since it is a quasi-matched system (50Ω on the spectrum analyser and 50Ω at the other end of the line), we can just subtract 34dBΩ(50Ω) from 130dBμV to arrive at 96dBμA, a good level that you need for automotive application.

Explanations of the performance difference

A possible explanation of the performance difference between the two probes are given below.

A simplified current probe circuit is shown in Figure 9 [4]. One should note that this model is based on an RF current monitoring probe, rather than an injection probe, but the principle is the same. Because the current monitoring probe is connected with a 50Ω (as the input of a spectrum analyser), the self-inductance forms an L-C circuit with the 50Ω load. This means that the impedance of the current probe against frequency becomes flat after the corner frequency (In Figure 10).

Figure 9 (a) Simplified current probe equivalent circuit (b) Thevenin circuit
frequency response [4]
Figure 10 Current probe frequency response [4]

In [4], Smith talked about the impact of resistance on the current probe frequency response. Here, we look at the impact of self-inductance on the current probe frequency response. We simulated 2 self-inductance value while keeping the resistance value the same, Figure 11 demonstrates the impact.

Figure 11 (a) small self-inductance delays the L/R corner point (b) current probe frequency response between small and large self-inductance

Using the probe as a current monitoring probe, we set up a test to compare the performance between the two probes and the result is shown in Figure 12. Frequency span is from 10kHz to 5MHz.

Figure 12 (a) Test set-up of current monitoring probe(b) frequency response of
single and multi-turn probe

When using the probe as a bulk current injection probe, the simplified current probe circuit is then shown in Figure 13. The mutual coupling depends on the magnetizing current, which at low frequency is limited mainly by the 50Ω resistance. As frequency goes up, the self-inductance starts to limit the magnetising current. Therefore, multi- turn configuration has less mutual coupling compared with single-turn configuration as shown in the test results in Figure 14.

Figure 13 Simplified circuit for current injection probe
Figure 14 (a) Test set-up of current injection probe(b) frequency response of single and multi-turn probe

For the single turn configuration of the current injection probe, the corner point is at roughly 700kHz. This explains what is shown in Figure 5.

After 40MHz, the interwinding capacitance starts to take effect, that’s why in Figure 6, the performance of the multi-turn configuration winding starts to drop. At higher frequency, the L-C tank circuit behaviour of the multi-turn configuration means the output is oscillating.

Reference

[1]  M. Zhang, “EMC Compliance,” 2021. [Online]. Available: http://emccompliance.co.uk/a-low- cost-bulk-current-injection-test-set-up.

[2]  A. Nielsen, “InCompliance Magazine,” 12 2021. [Online]. Available: https://incompliancemag.com/article/application-of-thrifty-test-equipment-for-emc-testing/.

[3]  Frederic Lafon;Younes Benlakhouy;Francois De Daran, “ResearchGate,” [Online]. Available:https://www.researchgate.net/publication/280094695_INJECTION_PROBE_MODELING_FOR _BULK_CURRENT_INJECTION_TEST_ON_MUL TI_CONDUCTOR_TRANSMISSION_LINES .

[4]  D. Smith, “Current probes, more useful than you think”.

When Common-mode Chokes Fail to Work

by Dr. Min Zhang, the EMC Consultant

Download link provided

The basic structure of an inductor is simple. Wind an enamelled wire around some magnetic core material will give you an inductor. But there are many different types of magnetic core material such as ferrite, powdered iron. The shape of the core can be toroid, E-shape and many more. The winding can be a single strand conductor, or multi-strand (rope-type) winding, or even a Litz wire. Engineers should select the right choice of inductor for their specific applications.

For example, nanocrystalline materials have become popular for inductor/common mode choke due to their performance in the broadband spectrum. But for motor drive application or high power switched mode power supply (SMPS) application, where EMI issue often starts with a few kHz, Manganese-Zinc or iron-powdered core is a better choice.

If you increase the number of turns of an inductor’s winding, you would expect the inductance value increase. In fact, you would expect the inductance value increase a lot since the relationship between the inductance and the number of turns is defined in Eq. 1. As it can be seen, the inductance is proportional to the n2.

L=n2Akμ0 (Eq.1)

where n is the number of turns of a winding, A is the cross-section area, k relates to the geometry of the coil of an inductor, μ0 is the permeability of free space.

In reality, however, this is often not the case. As the number of turns increases, so is the turn-to-turn capacitance of the winding. Increased turn-to-turn capacitance shifts the resonant frequency of an inductor to a lower frequency point, meaning the capacitance part of an inductor starts to dominate. In fact, this is one of the main reasons that engineers sometimes find an inductor/common mode choke (CMC) shows little impact in a design.

A case study is presented here to demonstrate the point we made. In Figure 1, a two-stage filter featuring two CMCs was designed to suppress noise in the frequency range of 20 to 30 MHz. The datasheet of the CMCs suggests good attenuation in the frequency range of interest, however, when the circuit was tested, engineers found the filter didn’t suppress the noise as they had hoped. The CMC is a nanocrystalline core with a ‘rope’ type winding structure. The first suggestion we made is to remove the two CMCs from the circuit and re-tested the board EMC performance.

Figure 1 two CMCs used in a two-stage filter for a DC-DC converter

To the engineers’ surprise, removing the CMCs improved the noise performance in the frequency range between 20 and 30 MHz by at least 6 dB. In the lower frequency range between 150kHz and 1 MHz, however, the noise performance was getting worse. We didn’t have the test result in hand, but for demonstration purposes, see below

Figure 2 The effect of the CMCs in this circuit

It is not a surprise that the CMCs didn’t work in the designed frequency range, as from 20 MHz, the winding capacitance due to the structure of this CMC dominates. In the lower frequency range, the leakage inductance of the CMC has an impact, this explains why removing the CMCs, the lower frequency EMC performance was getting worse. 

Changing the two CMCs to a ferrite core with less turns of winding solved the problem. 

Skin effect, eddy current and proximity effect are all related to frequency. As frequency increases, RF current tends to travel on the very outer thin layer of a conductor, hence the name ‘skin effect’. Engineers should be aware that these effects not only significantly increase the loss of an inductor, they also have an impact on the EMC performance. 

Ferrite Cores Basics

By Dr. Min Zhang, the EMC Consultant

Mach One Design Ltd

Ferrite materials such as Manganese-Zinc (MnZn) or Nickel-zinc (NiZn) are often found in the core material of an inductor. They are also popular materials for a range of inductive components called ferrite cores (as shown in Figure 1). Ferrite cores are extremely useful in suppressing RF noise on cables. During the product development stage, they are often used for quick troubleshooting and problem fixing. For a product that is close to the market launch deadline where iteration of the board design is impossible, putting a ferrite core on cables sometimes is the only cost-effective way of getting the product pass the EMC limit.

Ferrite cores can be used on single wire (as a differential-mode impedance) or a bundle of wires (as a common-mode impedance). A single-turn feedthrough configuration sometimes provides sufficient attenuation on the line. But most of the time, you might need to put multiple turns of a cable through a ferrite core so as to increase the impedance, as the impedance (inductance) value of a ferrite core is proportional to the square of the number of turns.

Figure 1 Ferrite cores for round cables

Engineers should be aware that although the core materials are often the same, different cores work in different frequency ranges depending on the manufacturing of these cores. Manufacturers often have specific cores for a specific frequency range. Make sure to use the right cores for the right job. For instance, if it is the medium frequency range noise between a few MHz and 30 MHz that you want to suppress, find a ferrite core whose impedance peaks in this frequency range. Figure 2 demonstrates ferrite cores on a cable (DC side) inside the cabinet of a three-phase uninterrupted power supply (UPS) system. In this case, noise level between 10 MHz and 30 MHz is quite high in the system, therefore a 31 material which works best in the same frequency range is selected to suppress the noise.

Figure 2 Demonstration of using ferrite cores on cables

Although ferrite cores are useful for suppressing the RF noise on the cable, they cannot replace a properly designed inductor. In environments where vibration and shocks are prevalent, ferrite cores need to be secured by cable ties or other means. In applications such as automotive products, using multiple turn ferrite cores are not allowed because of the limit of the bending radius of a cable. In general, a well-designed inductor is preferred. Ferrite cores are useful as a last resort in the design and development stage or the production volume of the products is very small.