**Here’s a less time-consuming way to maintain magnetic card reader and card reliability in a variety of noisy electronic environments.**

Plastic magnetic swipe cards are the principal means of establishing personal identity, processing financial transactions, and proving security level for access to secure corporate and military installations. Given the ubiquity of magnetic card readers (MCRs) and the harsh environments in which they’re used, embedded systems designers face daunting challenges.

in maintaining the reliability of their MCR-based systems, especially in the face of various levels and types of electronic noise.

One size does not fit all

One of the most crucial parts of any MCR system is the magnetic read head (MRH). When a card is swiped, the MRH converts the stored data in the card’s magnetic stripe to a voltage. Other MCR blocks process the converted voltage to extract the stored data. Large differences in magnetic field strengths from one card to another and differences in swipe speeds from one person to another make designing an MCR a challenging task.

Adding to the MCR design difficulty are the MRH data sheets, which do not fully specify the frequency-dependent components and are often vague when specifying other key parameters. In some cases the data-sheet specifications of two similar heads from two different manufacturers differ significantly in the list of parameters specified and those omitted. These differences are especially troublesome when you are trying to minimize noise issues in an MCR system and make designing an optimum card-reading system difficult and time-consuming.

This article outlines a strategy to resolve these specification issues, and then explains how to overcome the noise issues in an MCR using a secure microcontroller optimized for the task. One can certainly use Maxwell’s field equations, the geometry of the MRH, and the boundary conditions to predict the MRH output-voltage behavior. However, this approach is complicated and provides limited insights for circuit analysis, design, and debugging. Instead, we propose characterizing the MRH first and then using basic circuit theory and a simple circuit simulator to analyze MCR behavior.

Magnetic-stripe card basics**Figure 1** shows a magnetic stripe card with three tracks. Several ISO/IEC standards define important card properties such as the physical size, exact location of the stripes, magnetic properties, and magnetic track data structures.1 Track 1 standards were created by the International Air Transportation Association (IATA). Track 2 standards were created by the banking industry (American Bankers Association, ABA), and Track 3 standards were created by the thrift-savings industry.

A two-frequency coherent phase (F2F) technique is used for encoding the data on magnetic stripe cards. As shown in **Figure 2**, the binary data is encoded along the track by magnetizing stripe areas with different polarities. The polarity of the transitions is arbitrary, since only the *relative space* between the transitions implies a binary 1 or a binary 0.

A binary 0 is encoded with a two-unit bar magnet, while a pair of one-unit bars represents a binary 1. Each bit occupies the same physical length on the stripe. A bit with an additional flux transition in the middle of its length is a binary 1.

The spectrum of a continuous signal with F2F coding contains two fundamental frequencies, f0 and f1, where f0 is the fundamental of the square wave for binary 0 and f1 = 2f0 is the fundamental of the square wave for binary 1, hence the name F2F. The average amplitude of the binary 0 waveform is twice that of the binary 1 waveform, A0 = 2A1.

**Figure 3** shows the combined spectrum of F2F encoded binary 0s and 1s normalized to f0. Note that most of the signal energy resides between f0 and 3f0. Thus, to get a good approximation of a rectangular waveform containing a series of F2F encoded binary 1s and 0s, it is enough to recover the two fundamentals (f0 and f1) and the 3rd harmonic of f0.

Moreover, due to varying binary patterns there will be other components below f0. However, we can see from Fourier analysis that the amplitudes of these components decrease quickly for decreasing frequencies. Thus, a bandwidth from 0.5f0 to 3f0 is adequate for recovering an F2F-encoded rectangular waveform.2

To estimate the minimum and maximum bit rates for f0 and f1, we need to know the swipe speed range and the track recording density. From ISO/IEC standards, the recording density of Tracks 1 and 3 is 210 bits/in (8.27 bits/mm), while that of Track 2 is 75 bits/in (2.95 bits/mm).

For calculating f0,min we take the slowest swipe speed supported and multiply it by the Track 2 density numbers. For f1,max we pick the fastest swipe speed supported and multiply it by the density of Tracks 1 or 3.

For target swipe rates of 2in/s to 100 in/s (5cm/s to 254cm/s), the range of f0 and f1 values is calculated as:

* Tracks 1 and 3:* f0,min = 0.42kbps and f1,max = 42kbps

*f0,min = 0.15kbps and f1,max = 15kbps*

**Track 2:**The importance of knowing f0,min and f1,max will become clear once we have the MRH model and study its transfer function.

Fundamentals of magnetic read heads and card readers

Swiping a magnetic stripe card past a stationary MRH results in a changing magnetic flux that produces a moving electric field. Thus, a voltage is induced at the MRH’s output. Figure 2 can be used to study the reading process. Starting from the top, a magnetic stripe moving past an MRH results in changing flux events that induce a voltage at the MRH’s output terminals. The open-circuit readback voltage without any electrical losses is given by the well-known expression:3

Where:

- E(x̅) = open-circuit voltage.
- K = a constant relating the effects of magnetic-stripe velocity, head width, and the number of coil turns in the MRH.
- H(x, y) = field function of the read head.
- M[(x-x̅), y] = magnetic-stripe material magnetization.
- y1 = spacing from the head to the top of the magnetic-stripe.
- y2 = spacing from the head to the bottom of the magnetic-stripe.

Clearly, this equation is highly complicated and not intuitive for circuit analysis and design, but we can use the basic principles to determine a model as follows:

The MRH transfers magnetic energy to electric energy. Since the MRH’s input is a changing magnetic field and its output is a changing electric field, the model should contain at least one inductive element, Lh, and one capacitive element, Ch. In real systems some energy is always spent during the transformation. Thus, the model must also contain a resistive element, Rh. In practice, an MRH will not only have Ch across its two terminals, but it will also have an external impedance, Zo. from, for example, connecting wires, PCB traces, IC pins, probes, etc.

A model corresponding to the *n*th harmonic frequency, fn, is shown in **Figure 4a**, which then is simplified as **Figure 4b**.3,4,5 The transfer function of the 2nd-order circuit in Figure 4b is easily calculated as:

Note that the above transfer function does not contain any mechanical or magnetic terms, e.g., the swipe speed, head geometry, head and stripe separation, or the stripe magnetic properties. Thus, the transfer function is more intuitive for circuit design.

To further simplify things, we propose using a lumped model characterized at the highest system frequency instead of limiting the model to the swipe speeds.

Next we compare the electrical specifications of MRHs from some leading manufacturers. **Table 1** lists the key specifications that are needed for the model of Figure 4b. Notice the different amount of detail. While both Manufacturers A and C specify several electrical parameters, Manufacturer B specifies only one: peak-to-peak head readout level.

The following questions may arise about the missing information.

**Head inductance (Lh).**How does Lh behave over a larger frequency range? How does Lh behave when carrying currents other than what is specified?**Head DC resistance (Rh).**What voltage level is applied across the head terminals?**Head read output level (VO(P-P)).**What type of test card is used? What is the card swipe speed? What is the load across the head?**Head capacitance (Ch).**What is the capacitance between the two head terminals? Does it change with frequency?

To appreciate the importance of the above parameters, we examine the transfer function’s denominator and find its roots by setting it to zero:

To keep expressions simple and better understand the second-order behavior, several network analysis books use standard forms to write equations.6,7 One standard uses the form:

whose roots are:

Where α is the damping attenuation:

ωo is the resonance frequency:

Therefore, depending on the values of α and ωo, the roots of the natural response can be *real*, *complex*, or *imaginary*. For readers who are familiar with other standard forms, we now define the damping factor as ζ =α/ωo (note: quality factor Q = 1/2ζ) and use the other standard form:

whose roots are:

When a nonzero forcing function (such as a step, a ramp, or an impulse) is applied to the system, the location of the roots in the s-plane directly affects the settling behavior. **Figure 5** shows the settling behavior for various ζ values when a step is applied at t = 0. Specifically, the settling behavior is categorized as:

ζ > 1 → *overdamped*

ζ < 1 → *underdamped*

ζ = 1 → *critically damped*

ζ = 0 → *undamped or oscillatory*

From Figure 5 we observe that in an *underdamped* system, ringing occurs that can cause reading errors due to false peaks and false zero crossings. However, if the system is drastically *overdamped*, timing errors can occur from slow settling and reading errors can occur from shifts in the peaks. After analyzing an MRH’s time-domain behavior, we next look at its frequency-domain behavior.

**Figure 6** shows the frequency response of the transfer function, Tn(s), which is normalized to its resonance frequency, ωo. We observe peaking as we approach the system resonance frequency. This is due to the intrinsic nature of the circuit shown in Figure 4b, in other words, a parallel RLC. Depending on the swipe speed, this peaking can also cause reading errors.

Recall that when trying to recover F2F-encoded binary data, we need the two fundamental frequencies, f0 and f1, and at least the 3rd harmonic of f0. From Figure 3 we see that most of the signal energy is in the vicinity of 0.5f0 to 3.5f0, while a small portion is around 6f0.

What will happen to the recovered F2F waveform if higher harmonics were gained up? From Fourier analysis we know that the recovered waveform shape will change as the magnitudes of the higher harmonic coefficients change. Thus, for some cases the gain peaking shown in Figure 5 can reach a point where the 3rd and the 6th harmonics are amplified to such a level that the recovered signal is severely distorted. Any distortion that results in false peaks and zero crossings will lead to reading errors.

The above point is emphasized in **Figure 7**, which mathematically shows MRH output voltage for two different gains at higher harmonics: solid blue for the unity gain and orange for a gain of two. The dotted black lines are the zero crossing detector hysteresis limits. Clearly, as the gain doubles, the MRH output signal in red shows more distortion, false peaks, and zero crossings.

Furthermore, the MRH will not only experience disturbances due to varying card-swipe speeds, it will also see disturbances at much higher frequencies that might be present in the overall system, for example, a high-frequency system clock. Because of gain peaking, this too can result in signal distortion and possible reading errors. Thus, for designing an optimum card-reading system, it is crucial to know the frequency behavior of the MRH beyond the swipe rates. One must characterize the MRH frequency behavior at least to the highest system frequency.

Characterizing various read heads

We used a commercially available impedance/gain-phase analyzer to find the equivalent circuits of several MRHs from different manufacturers. The characterization included single-, double-, and triple-track MRHs that were used in the MCR based on a MAXQ1740 secure microcontroller. As 12MHz is the maximum system clock frequency for the MAXQ1740, each MRH was characterized from 100Hz to 12MHz (100Hz is analyzer’s limit). **Table 2** shows parameter averages for triple-track MRHs.

Analyzing the measured parameters

Comparing the parameters in Table 2, we see that MRH 1 and MRH 3 are similar. The relative differences between their parameters are ΔLh ~ 3.6%, ΔRh ~ 0.7%, and ΔCh ~ 7.5%. For MRH 2 and MRH 4, the relative differences in their parameters are ΔLh ~ 1.2%, ΔRh ~ 9.4%, and ΔCh ~ 83%.

Since Ch affects both α and ωo, for similar conditions we can expect the behavior of MRHs 1 and 3 to be similar. We can expect the behavior of MRHs 2 and 4 to track below their resonance frequencies, but then change as the frequencies reach close to, and beyond, their respective resonance points.

The last two points become obvious when we plot the transfer function’s frequency response for the characterized MRHs as shown in **Figure 8**. The load in Figure 8 is 1G, which results in a damping ratio of 0.03. The plots for MRHs 1 and 3 are virtually the same, while the plots for MRHs 2 and 4 show increasing differences around the resonance frequencies. The increase in magnitude could result in reading errors, as described earlier.

**Figure 9** shows MRH transfer functions for the frequency range of 150kHz to 300kHz, i.e., 3rd and 6th harmonics corresponding to the maximum card-swipe rate of 100in/s (254cm/s). We can see that as the swipe rates increase, so do the MRH transfer-function magnitude values. The main concern here is that if higher harmonics are gained up beyond a point, false zero crossings and peaks can occur, as shown in Figure 7. Also, if signals larger than the maximum allowed appear at the interface between the head and the card reader’s inputs, then reading errors can occur.

Two factors cause a larger signal. First, a faster swipe increases the rate of magnetic flux change. This, according to Faraday’s law, induces a larger inductor voltage, resulting in a larger inductor current. Second, a larger current flowing through a larger impedance results in a larger output voltage, in accordance with Ohm’s law.

Within the card swipe-rate range we need to limit the peaking to less than or equal to 20, which is the ratio between the maximum and minimum gains of the MAXQ1740 magnetic card reader. Figure 9 shows that the impedance change for MRHs 1 and 3 is less than 20, but the change for MRH 2 and MRH 4 is nearly 30 and exceeds the limit of 20.

What will happen if a damping resistor is added at the output of the MRH? **Figure 10** shows the transfer function plots for three arbitrarily different external loads values: 100kΩ, 10kΩ, and 1kΩ. We see in Figure 10 that for lower-value external resistors, the peaking is reduced compared to that shown in Figure 9. Note that for 1kΩ loads the gain at the 3rd harmonic is severely reduced for all four MRHs. This can be a problem. With 100k loads, for MRHs 2 and 3, the gains peaks at the 3rd harmonic, while for MRHs 2 and 3, the gain peaks at the 6th harmonic. The main point is that we cannot arbitrarily pick the Ro values.

When using external resistor Ro across the MRH terminals, it’s important to ensure that the damping ratio, ζ, stays as close to the unity as possible. **Figure 11** plots ζ vs. Ro for the four characterized MRHs. For ζ =1, we need Ro ≈ 12kΩ for both MRHs 1 and 3; Ro ≈ 22kΩ for MRH 2; and Ro ≈ 28kΩ for MRH 4. Figure 12 shows that transfer function with optimum load values. Comparing **Figure 12** to Figure 10, we note that the gain does not peak at the 3rd harmonic and stays close to unity.

While the maximum Ro is set by ζ=1, the minimum Ro value depends on the minimum signal supported and the head DC resistance, Rh. As a general rule, keep Ro ≥ 5Rh so that Ro in parallel with Rh will not attenuate the head output signal by more than 20%.

There are several key points to remember. First, due to parallel RLC, the transfer function peaks around the resonance frequency, ωo. Therefore, limit this peaking for the range corresponding to the 3rd and the 6th harmonics of card swipe rate, e.g., 150kH to 300kHz for the card swipe-rate range of 42kH to 50kHz. Second, the system behavior can be adjusted by placing Ro across the head reader’s terminals. Changing Ro changes the damping ratio, ζ. Finally, select Ro value to make the system critically damped and let the lead wiring and PCB routing set the Co value.