Impact of cable loss on automatic test equipment
Abstract: At present, many test companies design, manufacture, and sell automatic test equipment (ATE) with a large number of pins. These test devices have very complex integrated circuits that drive each pin of the device. A test equipment may have as many as 4096 pins. It can be seen from Figure 1: Each pin usually has a corresponding driver, comparator, load, and sometimes even requires a parameter test unit (PMU). These circuits are connected to the test pins via cables. In order to reduce costs, suppliers may choose poorer quality cables. And any cable, especially the poor quality cable, will cause loss, thereby reducing the final performance of the test equipment.
Figure 1. Typical block diagram of a test equipment (DUT)
Definition of cable loss The typical coaxial cable shown in Figure 2 has two main types of loss: skin-effect loss and dielectric loss.
Figure 2. Typical coaxial cable
Skin effect loss High-frequency signals are transmitted along the surface inside the conductor (shown in Figure 2). This phenomenon is called skin effect loss. The skin depth (δ) is defined as:
In the formula, ω is the frequency and the unit is rad / s; µ is the magnetic permeability of the conductor and the unit is H / m; Ï is the resistivity of the conductor and the unit is ohm • m. The skin effect causes the resistance Rl and inductance Ll per unit length of the wire to increase proportionally with the square root of the frequency. The formula for calculating the resistance per unit length is:
w is the wire width. For a round cable with radius r, its width is 2Ï€r. The resistance of the return path also needs to be considered, as this impedance is usually much smaller than the resistance of the forward path and can be ignored.
Dielectric Loss In Figure 2, dielectric insulators also produce cable losses related to frequency. The dielectric constant (ε) is defined as:
Where ε 'is the real part of the dielectric constant; tan δ represents the imaginary number, or loss tangent, which is the dielectric loss factor. Because the dielectric insulator affects the capacitance of the cable, the equivalent capacitance per unit length of the cable will change from (Cl) to Cl (1 + jtanδ).
The total cable loss considers the skin effect loss and the dielectric loss. The ideal model of the unit cable can be simplified as shown in Figure 3, including the above loss.
Figure 3. Simplified cable model
In Figure 3, we define the transmission coefficient as jk = √ZK, Z is the distributed series resistance, and Y is the distributed parallel admittance. In this situation:
After using Taylor series expansion, the approximate simplified equation can be obtained as follows:
ZO is the characteristic impedance of the transmission line, εr is the relative dielectric constant, and c is the speed of light.
What we ultimately need is the cable gain, H (f) = e-jkl, where l is the cable length. Using the above formula, you can get:
among them:
and
Through the above calculations, the following simple conclusions can be obtained: Skin effect loss (α1) plays a leading role in low-frequency loss (Figure 4) Dielectric loss (α2) plays a leading role in high-frequency loss (Figure 4) Actual cable H (f ) Is slightly different from the above approximate formula. For automatic test equipment, this approximate formula can provide sufficient accuracy, and the cable attenuation in these applications can be increased up to 6dB.
Figure 4. Typical characteristics of cable skin effect loss (inner conductor), dielectric loss, and return path (outer conductor) loss
Figure 4 shows the basic characteristic curves of various losses in a typical coaxial cable. Inside the coaxial cable is a copper wire with a characteristic impedance of 50Ω, and the outer layer is a braided metal conductor. Each type of cable loss has different characteristics, but the change trend is consistent with Figure 4.
Cable Loss Summary The purpose of this application note is not to provide a strict set of mathematical methods for calculating cable loss—these can be obtained from textbooks. The derived equation is used to prove the characteristic curve shown in FIG. 4. The following conclusions can be drawn from the above analysis: All cables generate losses, which ultimately limit system performance. The loss depends on the cable quality and specifications. Cable loss mainly includes: a. Skin effect loss plays a major role in low-frequency signals.
b. Dielectric loss plays a major role in high-frequency signals.
c. The return path loss is small and can be ignored in most cases.
d. Losses of connectors, relays and other output nodes or DUT wiring.
Cable loss and cable cost Figure 5 shows the loss characteristics of various typical cables. Table 1 compares the cost and loss of some cables.
Figure 5. Loss of different cables
Table 1. Price per foot of flexible coaxial cable from the same manufacturer
Note: Compared with inferior cables, the price of high-quality cables has increased exponentially, possibly up to 20 times (Figure 5, Table 1). ATE manufacturers prefer to use low-cost cables, but such cables can degrade system performance. If the pin electronics does not have cable compensation, the cable loss cannot be corrected. When using high-loss cables, it is necessary to replace low-cost, narrow-band, low-power drivers with high-cost, broadband, and high-power pin drivers to improve the system design margin. Using 4096 cables in a test facility, the cost per meter of cable will be between $ 5325 and $ 92,979 (Table 1). Add cable compensation to the pin electronics in the test equipment. Taking 4096-pin devices as an example, each device can save $ 92,979-$ 5325, or $ 87,654. The above cost price is based on the information provided in Table 1. Cable prices of different manufacturers may vary greatly. But from these figures, it can be seen that the expensive price of the cable. Therefore, it is very important for equipment manufacturers to choose low-cost cables. Table 1 lists the cables as flexible cables. Semi-rigid and all-steel cables have the best performance. The price of such cables is about $ 30 per foot, which is three times or more the best flexible cables. Because the cost of these cables is too high, manufacturers will not choose. As the operating frequency of the test equipment increases, cable compensation must be used. At present, the working speed of high-end test equipment exceeds 1Gbps. Impact of cable loss on performance For test equipment operating in the 200 Mbps range, cable loss has little effect. When the rate exceeds 500Mbps, the performance of the entire signal path, circuit, cable, and pin needs to be carefully analyzed to ensure that each pin gets the correct measurement index. The following lists the important indicators of the test equipment: The DC level accuracy of the waveform The rise and fall times The maximum trigger rate The minimum pulse width edge transmission delay accuracy and matching transmission deviation, for example, transmission deviation and minimum pulse width, amplitude, common mode voltage The choice of cable will directly affect the above indicators. To improve the trigger rate, regardless of the bandwidth of the cable driver, cable loss will become the main factor restricting the performance of the test equipment. This problem can be clearly seen from Figures 6 and 7.
Figure 6. Step response of short cable / high-quality cable
Figure 7. Step response of long cable / inferior cable
Most engineers already know the step response results shown in Figure 6 and Figure 7, but still need to pay attention to the following matters: t0 means the time to rise to 50% of the full width of the waveform. According to experience, the 10% to 90% rise time is approximately 28.6 x t0. It can be seen from the two waveforms that the rise time differs greatly under two different cable lengths or qualities. The roll-off characteristic has a greater impact on the maximum trigger rate, minimum pulse width, and bandwidth. The degradation of the signal path can be clearly seen from the figure above. The signal degradation has nothing to do with the actual driver. In this case, we use a circuit with infinite bandwidth step response, it is the cable that limits the rise time of the response. The higher the speed and the longer the cable, the more serious the problem. All cables, regardless of cable length and quality, will exhibit the characteristics shown in Figure 6 and Figure 7 to a certain extent. It is necessary to find a solution to the cable loss in order to make full use of the bandwidth of the driver, otherwise, only high-quality cables can be used, and the increase in cost has little effect on improving the system performance of the application. Designing cable compensation in the circuit can solve the problem of cable loss. Summary The cables used in high-speed test equipment will seriously affect the overall performance of the system and ultimately restrict the system specifications. Due to the large price differences between different cables, most high-speed test equipment use inferior cables with large losses. When the rate is close to or exceeds 1Gbps, the designer must consider the cable loss. The use of broadband drivers also cannot compensate for the loss of the cable, so the cable becomes a key factor limiting system performance.
In order to make full use of the performance of test equipment with a bandwidth greater than 1Gbps, the cable loss problem must be solved. Thankfully, an effective solution to the cable compensation problem has been obtained.
Figure 1. Typical block diagram of a test equipment (DUT)
Definition of cable loss The typical coaxial cable shown in Figure 2 has two main types of loss: skin-effect loss and dielectric loss.
Figure 2. Typical coaxial cable
Skin effect loss High-frequency signals are transmitted along the surface inside the conductor (shown in Figure 2). This phenomenon is called skin effect loss. The skin depth (δ) is defined as:
In the formula, ω is the frequency and the unit is rad / s; µ is the magnetic permeability of the conductor and the unit is H / m; Ï is the resistivity of the conductor and the unit is ohm • m. The skin effect causes the resistance Rl and inductance Ll per unit length of the wire to increase proportionally with the square root of the frequency. The formula for calculating the resistance per unit length is:
w is the wire width. For a round cable with radius r, its width is 2Ï€r. The resistance of the return path also needs to be considered, as this impedance is usually much smaller than the resistance of the forward path and can be ignored.
Dielectric Loss In Figure 2, dielectric insulators also produce cable losses related to frequency. The dielectric constant (ε) is defined as:
Where ε 'is the real part of the dielectric constant; tan δ represents the imaginary number, or loss tangent, which is the dielectric loss factor. Because the dielectric insulator affects the capacitance of the cable, the equivalent capacitance per unit length of the cable will change from (Cl) to Cl (1 + jtanδ).
The total cable loss considers the skin effect loss and the dielectric loss. The ideal model of the unit cable can be simplified as shown in Figure 3, including the above loss.
Figure 3. Simplified cable model
In Figure 3, we define the transmission coefficient as jk = √ZK, Z is the distributed series resistance, and Y is the distributed parallel admittance. In this situation:
After using Taylor series expansion, the approximate simplified equation can be obtained as follows:
ZO is the characteristic impedance of the transmission line, εr is the relative dielectric constant, and c is the speed of light.
What we ultimately need is the cable gain, H (f) = e-jkl, where l is the cable length. Using the above formula, you can get:
among them:
and
Through the above calculations, the following simple conclusions can be obtained: Skin effect loss (α1) plays a leading role in low-frequency loss (Figure 4) Dielectric loss (α2) plays a leading role in high-frequency loss (Figure 4) Actual cable H (f ) Is slightly different from the above approximate formula. For automatic test equipment, this approximate formula can provide sufficient accuracy, and the cable attenuation in these applications can be increased up to 6dB.
Figure 4. Typical characteristics of cable skin effect loss (inner conductor), dielectric loss, and return path (outer conductor) loss
Figure 4 shows the basic characteristic curves of various losses in a typical coaxial cable. Inside the coaxial cable is a copper wire with a characteristic impedance of 50Ω, and the outer layer is a braided metal conductor. Each type of cable loss has different characteristics, but the change trend is consistent with Figure 4.
Cable Loss Summary The purpose of this application note is not to provide a strict set of mathematical methods for calculating cable loss—these can be obtained from textbooks. The derived equation is used to prove the characteristic curve shown in FIG. 4. The following conclusions can be drawn from the above analysis: All cables generate losses, which ultimately limit system performance. The loss depends on the cable quality and specifications. Cable loss mainly includes: a. Skin effect loss plays a major role in low-frequency signals.
b. Dielectric loss plays a major role in high-frequency signals.
c. The return path loss is small and can be ignored in most cases.
d. Losses of connectors, relays and other output nodes or DUT wiring.
Cable loss and cable cost Figure 5 shows the loss characteristics of various typical cables. Table 1 compares the cost and loss of some cables.
Figure 5. Loss of different cables
Table 1. Price per foot of flexible coaxial cable from the same manufacturer
| Cable | Loss at 900MHz (dB ​​/ m) | Cost per Meter ($) |
| RG174 | 0.75 | 1.3 |
| RG142 | 0.382 | 14.6 |
| RG400 / U | 0.3492 | 15.11 |
| RG232 / U | 0.4589 | 10.4 |
| R393 / U | 0.296 | 22.7 |
| RG58 low loss | 0.3691 | 1.46 |
| RG58 / U | 0.531 | 1.14 |
| RG8X | 0.25 | 1.79 |
| RG8 | 0.14 | 14.3 |
Note: Compared with inferior cables, the price of high-quality cables has increased exponentially, possibly up to 20 times (Figure 5, Table 1). ATE manufacturers prefer to use low-cost cables, but such cables can degrade system performance. If the pin electronics does not have cable compensation, the cable loss cannot be corrected. When using high-loss cables, it is necessary to replace low-cost, narrow-band, low-power drivers with high-cost, broadband, and high-power pin drivers to improve the system design margin. Using 4096 cables in a test facility, the cost per meter of cable will be between $ 5325 and $ 92,979 (Table 1). Add cable compensation to the pin electronics in the test equipment. Taking 4096-pin devices as an example, each device can save $ 92,979-$ 5325, or $ 87,654. The above cost price is based on the information provided in Table 1. Cable prices of different manufacturers may vary greatly. But from these figures, it can be seen that the expensive price of the cable. Therefore, it is very important for equipment manufacturers to choose low-cost cables. Table 1 lists the cables as flexible cables. Semi-rigid and all-steel cables have the best performance. The price of such cables is about $ 30 per foot, which is three times or more the best flexible cables. Because the cost of these cables is too high, manufacturers will not choose. As the operating frequency of the test equipment increases, cable compensation must be used. At present, the working speed of high-end test equipment exceeds 1Gbps. Impact of cable loss on performance For test equipment operating in the 200 Mbps range, cable loss has little effect. When the rate exceeds 500Mbps, the performance of the entire signal path, circuit, cable, and pin needs to be carefully analyzed to ensure that each pin gets the correct measurement index. The following lists the important indicators of the test equipment: The DC level accuracy of the waveform The rise and fall times The maximum trigger rate The minimum pulse width edge transmission delay accuracy and matching transmission deviation, for example, transmission deviation and minimum pulse width, amplitude, common mode voltage The choice of cable will directly affect the above indicators. To improve the trigger rate, regardless of the bandwidth of the cable driver, cable loss will become the main factor restricting the performance of the test equipment. This problem can be clearly seen from Figures 6 and 7.
Figure 6. Step response of short cable / high-quality cable
Figure 7. Step response of long cable / inferior cable
Most engineers already know the step response results shown in Figure 6 and Figure 7, but still need to pay attention to the following matters: t0 means the time to rise to 50% of the full width of the waveform. According to experience, the 10% to 90% rise time is approximately 28.6 x t0. It can be seen from the two waveforms that the rise time differs greatly under two different cable lengths or qualities. The roll-off characteristic has a greater impact on the maximum trigger rate, minimum pulse width, and bandwidth. The degradation of the signal path can be clearly seen from the figure above. The signal degradation has nothing to do with the actual driver. In this case, we use a circuit with infinite bandwidth step response, it is the cable that limits the rise time of the response. The higher the speed and the longer the cable, the more serious the problem. All cables, regardless of cable length and quality, will exhibit the characteristics shown in Figure 6 and Figure 7 to a certain extent. It is necessary to find a solution to the cable loss in order to make full use of the bandwidth of the driver, otherwise, only high-quality cables can be used, and the increase in cost has little effect on improving the system performance of the application. Designing cable compensation in the circuit can solve the problem of cable loss. Summary The cables used in high-speed test equipment will seriously affect the overall performance of the system and ultimately restrict the system specifications. Due to the large price differences between different cables, most high-speed test equipment use inferior cables with large losses. When the rate is close to or exceeds 1Gbps, the designer must consider the cable loss. The use of broadband drivers also cannot compensate for the loss of the cable, so the cable becomes a key factor limiting system performance.
In order to make full use of the performance of test equipment with a bandwidth greater than 1Gbps, the cable loss problem must be solved. Thankfully, an effective solution to the cable compensation problem has been obtained.
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