ISSN 1063-7397, Russian Microelectronics, 2016, Vol. 45, No. 7, pp. 492–497. © Pleiades Publishing, Ltd., 2016.
Original Russian Text © V.D. Sadkov, A.V. Lopatkin, 2015, published in Izvestiya Vysshikh Uchebnykh Zavedenii, Elektronika, 2015, Vol. 20, No. 6, pp. 607–615.
Refined Model of Low-Impedance Film Resistors
with a Comb-Like Structure
V. D. Sadkov and A. V. Lopatkin*
Institute of Radioelectronics and Information Technologies, Alekseev Nizhny Novgorod State Technical University,
Nizhny Novgorod, 620078 Russia
Received March 3, 2015
Abstract—Using the methods of finite element and conformal mapping, analytical models with low and
ultralow resistance of the film resistors of the main types of comb-like (interdigital) structures with an arbi-
trary ratio between the surface resistivities of resistive and conductive films have been worked out. In the
resultant resistance, the resistances of comb-like and connecting electrodes are taken into account, as well as
the additional resistance caused by the passage of the current from the conductive to the resistive film and
vice versa. The conditions under which an interface between the films can be treated as an equipotential sur-
face are revealed. An equivalent circuit of low-impedance comb resistors, which are used as the sensors of the
current in the circuits of stabilization and control, as well as thermal and current protection.
Keywords: resistance of a low-impedance film resistor with a comb-like structure, contact resistance, equiv-
alent circuit of the film resistor
Film resistors with low and ultralow-impedance,
high thermal and temporal stability, low noise level,
high frequency-power characteristics, and a small
reproduction error of the nominals are widely used as
current sensors in the circuits of stabilization and con-
trol, as well as thermal and current protection [1–3].
The development of such resistors requires not only a
transition to more complex topologies but also careful
consideration of their contact resistances, including
the resistance of the contact electrodes and additional
resistance of the transition region of the current from
a conductive film to a resistive one and vice versa [4,
5]. This is caused by the sharp unevenness of the cur-
rent near the transition area along the length and
thickness of the films . The calculation of these
parameters in [4, 5] was carried out either with an
unacceptable accuracy (in practice), by using simple
relationships without accounting for the two-dimen-
sional structure, as well as the fields of the potentials
In this work, using the methods of finite elements
and conformal mapping, analytical models with the
low and ultralow resistance of film resistors with a
comb-like structure were worked out with allowance
for the connection electrodes and additional resis-
tance due to the transition of the current from a con-
ductive to a resistive film and vice versa.
Figure 1a shows the conventional comb-like struc-
ture . The structure in Fig. 1b allows one to advance
a little bit further into the range of resistances with low
The required resistance includes the resistance of
the comb electrodes, the resistance of the connec-
tions, and the additional resistance due to the transi-
tion of the current from a resistive to a conductive film
and vice versa. The position of the connecting con-
tacts relative to the electrodes of the conductive con-
tacts is arbitrary.
The comb structure’s resistance is formed by the
connection of the base elements (Fig. 2).
The size L is determined through the parameters of
the base elements
L= ne + (n + 1)a/2,
where n is the number of resistive strips.
For providing equipotentiality on the boundaries of
the base elements, size H should satisfy condition 
CALCULATING THE RESISTANCE
OF THE BASE ELEMENTS
We calculated resistances R
of the base elements
(Fig. 1) in a wide range of ratios of the parameters
0.057 (1.3 / ) 0.08 (1.3 / ) .