Conductor loss

Carsten, B. Calculating Skin and Proximity Effect, Conductor Losses in Switchmode Magnetics , 1995, PCIM Conference... 

The conductor losses can be found by evaluating R per unit length and using the expression for y or by using an incremental inductance rule, which leads to... 

Attenuation The decrease in amphtude of an electrical signal traveling through a transmission medium caused by dielectric and conductor losses. 

The relative permeability is a measure of how a magnetic field interacts with a material and can often be considered a constant for a given material. The net result of this skin effect is that conduction is limited to a thinner region of a metallization at higher frequencies. Consequently, the net conductor loss may appear lower if the skin effect is taken into account. In practice, conductor thickness of more than a few skin depths is of little value. However, the reader should note that at low frequencies, the skin depth becomes very large. 

This correction factor is plotted in Figure 2.1. In a perfectly smooth surface (no roughness), there is no increase in conductor attenuation as a result of roughness. If the roughness is 50% of the skin depth, there is a conductor attenuation increase of 1.21, or 21% increase in conductor loss over a perfectly smooth conductor, due to roughness. If the roughness equals the skin depth, the increase in conductor attenuation is 1.61, or 61%. 

Baker-Jarvis, J. et al., NIST Technical Note 1520 Dielectric and Conductor-Loss Characterization and Measurements on Electronic Eackaging Materials, National Institute of Standards and Technology, 325 Broadway, Boulder, CO, 80303. 

Interdigital capacitors offer high-quality factors because dielectric losses of the substrate and the surrounding air (if printed on the surface) are very low. Conductor losses mainly contribute to the overall loss. 

The overall quality of a capacitor can be determined using Equation 9.29. Qs represents the conductor loss in the electrodes. 

After optimization with an electromagnetic simulator, filters were manufactured using DuPont Tape 951. Silver metallization was applied for lowest conductor losses. Top and bottom groimd plane metallization was Ag-Pd (for solderability). Multiple ground and signal interconnections were achieved witii an array of solder bumps (BGA). Figure 9.73 depicts the LTCC filter element with the dimensions 14 x 9 x 3 mm (14 layers). 

Brist, Gary, Hall, Stephen, Clauser, Sidney, and Liang,Tao, Non-Clasacal Conductor Losses Due to Copper Fail Roughness andTreatment, ECWC10/IPC/APEX Conference, February 2005. 

Embroidered (5) Conductive High conductor loss due to Locher and... 

High frequency transmission loss (1/Q) is expressed as the relationship between dielectric loss (l/Qa) and conductor loss (1/Qc)- As shown in Figure... 

However, conductor loss depends on the resistance (surface resistance) of the conductor. As the frequency increases, there is a tendency for the current to concentrate in the surface parts of the conductor. The part where the current flows is known as skin depth (the depth where current density falls to 1/e = 0.37 of its value at the surface), and it decreases in inverse proportion to the square root of the frequency. Surface resistance Rs is determined by skin depth d and conductor conductivity o as in the formula below. It is inversely proportional to the square root of conductor conductivity, and increases proportional to the square root of the frequency. 

Figure 1.5 (b) shows the frequency dependence of dielectric loss and conductor loss. It shows the result using a model with conductor thickness of 30 pm, width 8 mil (203.2 pm), tan 8 0.02, Cr 3.5, and characteristic impedance of 50 At frequencies lower than 1 GHz, conductor loss is more dominant than dielectric loss as far as signal attenuation is concerned. However, above 1 GHz, the impact of dielectric loss becomes all the more conspicuous with increases in frequency. 

Figure 1.5 The frequency dependence of dielectric loss and conductor loss (a) and dielectric loss in a circuit (b).

The major characteristic of LTCCs is that metals with low conductor resistance - Cu, Au, Ag and their alloys - are introduced into the ceramic as wiring, thus controlling conductor loss to a low level. As Table 2-1 shows, all the metals with low electrical resistance have a low melting point of around 1,000°C, and in order to allow cofiring with these metals, LTCC ceramics are required to be able to be fired at less than 1,000 C [1,2]. 

To reduce conductor loss in high frequency ranges, it is necessary to take an proach that reduces conductor resistance to the minimum (refer to Chapter 1). Since the inductance of the conductor inside increases at high frequencies, current flows only near the surface of the conductor layer. The thickness of the area where the current flows is called skin depth. Figure 10-1 shows the relationship between the frequency of each type of conductor and the skin depth. The relationship with skin depth ( ) is in accordance with the formula below, and there is a tendency for the skin depth to become shallower as the frequency increases with materials that are not magnetized. 

As indicated in the previous section, it is effective to reduce the surface roughness of the conductor in order to reduce conductor loss. For this reason it can be considered necessary to develop processes to print the conductor after flattening the cast green sheet by applying pressure, or processes to apply pressure to the conductor after printing to make the conductor wiring flat and so on. 

Figures 14.7a,b show the measured transmission (S j) and reflection (S ) coefficients of one particular CPW with length of 40 mm. Ripples can be observed in Figure 14.7a, which are a byproduct of minor impedance mismatch arising from the difference in initially estimated PDMS dielectric constant to the true dielectric constant. This minor mismatch is to be expected, as one of the aims of this process is to determine the true dielectric constant starting with a value defined in the data sheet. Since the reflection magnitude of Figure 14.7b remains below 10 dB at aU frequencies, it can be concluded that the impedance of the transmission line remains close to 50 O over the entire bandwidth. The transmission magnitude attenuates across the bandwidth at approximately 5.5 dB with additional loss at 20 GHz. This loss is high, but not excessively so. The components of loss would be associated with the conductor loss due to finite conductivity, this is small as gold behaves close to PEC at microwave frequencies, and dielectric losses originate from the PDMS substrate. The loss will have the form ...

Cable attenuation is a function of both the conductor loss and the dielectric loss. 

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