Adjustable Cable Equalizer Combines Wideband Differential Receiver with Analog Switches

Originally intended to carry LAN traffic, category-5 (Cat-5) unshielded twisted-pair (UTP) cable has become an economical solution in many other signal-transmission applications, owing to its respectable performance and low cost. For instance, an application that has become popular is keyboard-video-mouse (KVM) networking, in which three of the four twisted pairs carry the red, green, and blue (RGB) video signals.

Like any transmission medium, Cat-5 imposes transmission losses on the signals it carries, manifested as signal dispersion and loss of high-frequency content. Unless something is done to compensate for these losses, they can render the cables useless for transmitting high-resolution video signals over reasonable distances. Presented here is a practical technique to compensate for Cat-5 losses by introducing an equalizer (EQ), with eleven (11) switchable cable-range settings, at the receiving end of the cable. Because each setting of the EQ provides the proper amount of frequency-dependent gain to make up for the cable losses, the EQ-cable combination becomes suitable for high-resolution video transmission.

The first step in the EQ design is to derive a model for the Cat-5 frequency response. It is well known that the frequency response of metallic cable follows a low-pass characteristic, with an exponential roll-off that depends on the square root of frequency. Figure 1 depicts this relationship for lengths of Cat-5 from 100 feet (30.48 m) through 1000 feet (304.8 m), in 100-foot increments. In this illustration, it should be evident that the power loss at a given frequency is characterized by a constant attenuation rate (expressed in dB/ft).

Table I presents the Cat-5 equivalent voltage-attenuation magnitudes as a function of frequency for the same cable lengths as shown in Figure 1.

Table I. Voltage-attenuation magnitude ratios of Cat-5 cable. For example, 500 feet of cable attenuates a 10-MHz, 1-V signal to 0.32 V, which corresponds to about –9.90 dB (Figure 1).

Using the data in Table I, the frequency response for each cable length can be approximated by a mathematical model based on a negative-real-axis pole-zero transfer function. Any one of the many available math software packages with the capability of least-squares polynomial curve fitting can be used to perform the approximation. Figure 1 suggests that, for long cables at high frequencies—because of the steepening slope, exceeding 20 dB/decade—consecutive negative-real-axis poles are required to obtain a close fit, while at low frequencies—to fit the nearly linear slope—alternating poles and zeros are required. As an extreme example, the frequency response for 1000 feet of cable at 100 MHz is rolling off approximately as 1/f4, which can only be attained by a model having multiple consecutive poles.

Equalization is achieved by passing the signal received over the cable through an equalizer whose transfer function is the reciprocal of the cable pole-zero model’s transfer function. To neutralize the cable’s frequency-dependency, the EQ has poles that are coincident with the zeros of the cable model and zeros that are coincident with the poles of the cable model.

One of the properties of passive RC networks is that the alternating poles and zeros of their driving-point impedances are restricted to the negative real axis. This property also holds for those operational-amplifier circuits having a transfer function determined by the simple ratio of feedback-impedance to gain-impedance (Zf/Zg), where these impedances are RC networks. (The property does not hold for other cases, such as active RC filter sections that synthesize conjugate pole-pairs.)

For a practical equalizer design, we prefer that an EQ be based on a single amplifier stage in order to keep its adjustability manageable and to minimize cost and complexity. The equalizer to be discussed here uses RC networks of the former type, described by Budak, with alternating poles and zeros; but such a design precludes the use of a single amplifier stage to realize the consecutive zeros required to compensate for consecutive poles in the cable model at all frequencies. As a compromise that will provide good equalization for all but long cables at high frequencies, the design chosen uses a single amplifier to realize two zeros and two poles, alternating on the negative real axis.

Because equalization requires increased gain at the high end of the band, a low-noise amplifier is required. To avoid introducing significant errors due to amplifier dynamics, a large gain-bandwidth product is needed. For the specific design requirements of this application, the amplifier must have the capacity to perform frequency-dependent differential-to-single-ended transformations with voltage gain. The Analog Devices AD8129, just such an amplifier, is the heart of the basic frequency-dependent gain stage in the EQ. Figure 2 shows the dual-differential-input architecture of the AD8129, and its standard closed-loop configuration for applications requiring voltage gain.

As can be seen, the AD8129 circuitry and operation differ from those of the traditional op amp; principally, it provides the designer with a beneficial separation of circuitry between the differential input and the feedback network. The two input stages are high-impedance, high-common-mode-rejection (CMR), wideband, high-gain transconductance amplifiers with closely matched gm. The output currents of the two transconductance amplifiers are summed (at high impedance), and the voltage at the summing node is buffered to provide a low impedance output. The output current of amplifier A equals the negative of the output current of amplifier B, and their transconductances are closely matched, so negative feedback applied around amplifier B drives vout to the level that forces the input voltage of amplifier B to equal the negative of the input voltage of amplifier A. From the above discussion, the closed-loop voltage gain for the ideal case can be expressed as:

The EQ is designed using this gain equation, with RC networks for Zf and Zg. Its canonical circuit is depicted in Figure 3, which represents an EQ designed to compensate for a given length of cable.

In Figure 3, the high differential input impedance of the upper transconductance amplifier facilitates provision of a good impedance match for the signal to be received over the Cat-5 cable; the lower amplifier provides the negative feedback circuit that implements the frequency-dependent gain. The Bode plot for the circuit has a high-pass characteristic, as shown in Figure 4. Zn and Pn are the respective zeros and poles of the equalizer.

In the following analysis, where the pole-zero pairs in Figure 4 are sufficiently separated, the capacitors can be approximated as short- or open circuits. The pole- and zero frequencies are expressed in radians per second. At low frequencies, all capacitors are open circuits, and the gain is simply

This gain, set to compensate for flat (i.e., dc) losses, includes any loss due to matching and the cable’s low-frequency flat loss. It also provides the flat gain required to stabilize the AD8129 when equalizing short cables (to be covered in greater depth below).

Moving up in frequency, the lowest-frequency pole-zero EQ section, comprising the series-connected REQ and CEQ, starts to take effect, producing Z1 and P1. By approximating Cf and CS as open circuits, the following equations can be written:

The magnitude of the frequency response asymptotically approaches

as CEQ approaches a short circuit.

As frequency increases, CS begins to take effect, introducing another zero, Z2. The primary function of Cf is to keep the amplifier stable by compensating for CS. By initially approximating Cf as an open circuit (Cf