Ohmega-Ply® follows standard thin-film design rules.
[TABLE OF CONTENTS]



III) RESISTOR DESIGN

A) RESISTOR PARAMETERS

The resistance of a material is directly proportional to its length and inversely proportional to its cross-sectional area.

Eq. 1


where p is a constant of proportionality known as the resistivity and h is a constant and represents the thickness of resistor film.

Eq. 2


where Rs is sheet resistance (Ohm/square). The resistance value can be determined by sheet resistance and geometry of the resistor according to the formula above.

Eq. 3


where N is the number of squares (N = L/W )

Fig. 4



B) RESISTOR PATTERNS

i) bar type
  1. multiple squares ( N > or equal to 1 )
  2. partial square ( N < 1 )
Fig. 5





ii) shorting bar type

Fig. 6



ii) meander type

Basically, a meander resistor can be considered as a bar resistor with the exception of the corner squares (right-angle bends). Due to the change in current density at right-angle path, the effective number of squares is 0.559, which is commonly used in resistor design. A lot of complex resistors geometries can be determined by the conformal mapping techniques.

Fig. 7



C) RESISTOR ELEMENT SIZE

1) Long term reliability is a function of operating temperature. Like most electronic components, operating temperature (ambient temperature + temperature rise) is one of the most important factors that determine power rating of the component. As more power is dissipated through the resistors, the temperature of the resistor film increases which makes it more susceptible to thermal oxidation. Stability is measured by the change of resistance with aging. The figure below illustrates the relationship between different operating temperatures and change of resistance with respect to time.

Fig. 8



2) DESIGN PARAMETERS

Because the resistor film is a part of laminate, the physical and thermal characteristics of the substrate become major considerations. The heat dissipation of resistor film depends on:
  1. the size (area) of the resistor
  2. the circuit thickness and material type
  3. the circuit configuration (clad/unclad)
  4. ambient temperature
  5. the thermal conductivity of the substrate
  6. additional system cooling (e.g air-cooling, other heat sinking,etc)
a) Area

The power density is defined as the total power dissipated divided by the effective surface area. The power density of resistor element increases as element area decreases, all other conditions being the same. The graph ( experimental results ) below illustrates that for the same power input, the temperature rise depends on the area of the resistor.

Fig. 9



R1 = 25 Ohms area of R1 = 0.500 x 0.500 = 0.2500 in2
R2 = 25 Ohms area of R2 = 0.250 x 0.250 = 0.0625 in2
R3 = 25 Ohms area of R3 = 0.125 x 0.125 = 0.0156 in2
R4 = 25 Ohms area of R4 = 0.063 x 0.063 = 0.0039 in2
R5 = 25 Ohms area of R5 = 0.031 x 0.031 = 0.0010 in2

For the same power input, the temperature rise of R5 (smallest area) is the highest. In other words, the resistors with larger area can dissipate more power than a smaller one provided that all conditions remains the same. If space is available, design the resistors as large as possible.

b) & c) the substrate thickness & configuration (clad/unclad)
[TABLE OF CONTENTS]


 Fig. 10



Because the resistor is buried within layers, the physical and thermal characteristic of the substrate directly affect the manner of heat dissipation from the substrate e.g the thickness of the substrate and cladding (heat sinking effect). As shown in the above graph the temperature rise in the resistor (R1) is improved significantly when copper cladding (R2) is used.

CORE THICKNESS CLADDING
R1 = 250 Ohms 0.0025" 1R25/0 (UNCLAD)
R2 = 250 Ohms 0.0025" 1R25/1 (CLAD)
R3 = 250 Ohms 0.025" 1R25/0 (UNCLAD)
R4 = 250 Ohms 0.025" 1R25/1 (CLAD)
R5 = 250 Ohms 0.062" 1R25/0 (UNCLAD)
R6 = 250 Ohms 0.062" 1R25/1 (CLAD)