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ELECTROMAGNETIC SCIENCE

Review

Regulation and Control of Electromagnetic Field in

Radio-Frequency Circuits and Systems

Kaixue Ma

Tianjin Key Laboratory of Imaging and Sensing Microelectronic Technology

School of Microelectronics

Tianjin University

Tianjin 300072

China

Corresponding author: Kaixue Ma, Email: makaixue@tju.edu.cn.

Received November 3, 2022; Accepted August 21, 2023; Published Online September 20, 2023.

Abstract—Since the first demonstrations of radio-frequency (RF) circuits, the physics of the electromagnetic (EM) field and its regulation and control

with codesigned circuits, have become essential competencies of RF circuit designers. Leveraging advanced regulation or control methods, numerous

high-performance circuits have been developed at RF and millimeter-wave (mm-wave) frequencies. Three main methods of electromagnetic regulation

have been widely utilized, namely, the separation of electric and magnetic coupling paths, the manipulation of electromagnetic energy through the cou-

pling of multiple tanks or multiple resonators, and the regulation of electromagnetic fields in air cavities or meta-substrates. The separated coupling paths

of electric and magnetic fields provide guidance for designing a high-performance filter topology with a quasielliptical response through additional ze-

ros. The manipulation of the EM field through electrical and magnetic intercouplings of multitanks or multiresonators, such as are used in oscillators,

power amplifiers (PAs), etc., results in remarkable power efficiency, size reduction, and wide bandwidth. The regulation of electromagnetism through an

air cavity, patterned substrate, or metasubstrate reduces dielectric losses and size, especially when using a substrate integrated suspended line (SISL)

platform. Many excellent circuits have been reported based on SISL with low loss, high integration, and self-packaging. Here, we present state-of-the-art

cases that demonstrate the benefits of EM field regulation and control.

Keywords—Electromagnetic, Mixed coupling, Multiresonators and multitanks, Patterned substrate and metasubstrate, Radio frequency circuits,

Regulation and control, Separate electronic and magnetic coupling paths, Substrate integrated suspended line.

Citation—KaixueMa, “Regulation and Control of Electromagnetic Field in Radio-Frequency Circuits and Systems,”

Electromagnetic Science

vol. 1, no. 3, article no. 0030101, 2023. doi: 10.23919/emsci.2022.0010.



I. Introduction

With the advancement of wireless communication technolo-

gy and radio frequency (RF) systems, increasing demands

for miniaturization, low loss, and low cost are prompted for

integrated circuits and systems with higher performance

and compact size. Recently, various technologies for elec-

tromagnetic (EM) control in radio frequency circuits has

been extensively studied by our group and other research-

ers. Many circuits operating in RF or microwave regimes

have seen improved performance using electromagnetic

regulation and control. For example, the control technology

in [1] helped to achieve a low insertion loss and small size,

as well as controllable transmission zeros (TZs) for the fil-

ter design. Additionally, in [2], an enhanced quality-factor

(Q-factor) and wide tuning range were performed by intro-

ducing electromagnetic control theory for RF ICs. This type

of recently developed technology consists of the separation

and regulation of electric and magnetic coupling paths, the

regulation and control of electromagnetic energy, and elec-

tromagnetic control in the medium or substrate.

Commonly implemented methods of separating elec-

tric and magnetic coupling paths (SEMCP) filter topology,

as shown in Figure 1(a), include physical separation and

equivalent separation in electric, i.e., in equivalent or equa-

tion. The separation of physical electric and magnetic cou-

pling paths offers the benefits of simplifying the design, in-

tuitive analysis, and separate control of TZs. Equivalent

electronic and magnetic coupling paths can provide instruc-

tions and guidance to the filter designs according to the

equations on the required positions of TZs, return loss, and

more. Regarding the regulation and control of electromag-

netic energy in EM coupling proposed in [2], as shown in

Figure 1(b), this approach can be conducted by electrical

coupling, magnetic coupling regulation and control, and

mixed electromagnetic techniques that treat the coupled

capacitor, inductors or both as equivalent to an electric or

magnetic or electromagnetic energy storage device. This

combination offers outstanding advantages for silicon-

based circuits and systems, such as an enhanced Q-factor, a

wide tuning range, a remarkable figure-of-merit (FoM),

considerable efficiency and linearity, and a reduced core



Electromagnetic Science

vol. 1, no. 3, 0030101, September 2023

https://doi.org/10.23919/emsci.2022.0010

ELECTROMAGNETIC SCIENCE

packaging [13]–[30]. To expand the advantages of SISL,

several EM regulation methods have been presented to fur-

ther reduce the loss of substrate and metal, such as double-

sided interconnected strip line (DSISL) technology [16],

patterned substrates [16], and multiple inner boards [26].

Several methods are introduced to miniaturize the circuit

designs, such as loading dielectric blocks with high dielec-

tric constant material, quasilumped elements, and metasub-

strate [30]–[34].

The remainder of this article is organized as follows.

Section II introduces the theory of separate electric and

magnetic coupling paths, combined with analyzing the ba-

sic circuits and application cases. Section III discusses the

regulation technique of electromagnetic energy in multi-

tank circuits, including principles and some circuit designs

with enhanced performance. Section IV demonstrates the

regulation of EM in air cavities, patterned substrates, load-

ed dielectric substrates, or metasurface electromagnetics,

consisting of theories, guidance for utilizing this technolo-

gy, and some specific improved methods applied to circuit

design. The conclusion summarizes three main kinds of

regulation and control technologies for EM, presenting the

advantages of applying this newly developed technology.

II. Separating Electric and Magnetic Coupling

Path Regulation Theory and Circuits

1. Overview of the SEMCP topology

In recent years, the demand for available frequency chan-

nels has continuously increased, which results in more

stringent standards for high-performance microwave band-

pass filters (BPFs) used in communication systems. Re-

search on BPFs has long been one of the key directions in

microwave fields. Direct-coupled microwave BPFs and

cross-coupled BPFs [35] were introduced in the early

1950s; since then, much effort has focused on the synthesis

and design of BPFs with advanced topologies. Recently, as

a promising method to achieve high-performance filter re-

sponses, the SEMCP topology proposed by Ma in [1] in the

filter synthesis and design process has received significant

attention.

Regarding the EM regulation theory of the separating

electric and magnetic coupling paths in circuits, two main

methods have been implemented thus far, namely, physical

path separation and equivalent electric and magnetic cou-

pling path separation. The mechanism of physical path sep-

aration is mainly the introduction of two or even more par-

allel paths in physical space, i.e., an electric coupling path

and a magnetic coupling path, and additional TZs can be

generated through the EM coupling canceling between the

paths. In general, the electric coupling path can be realized

by an equivalent capacitive element, while the magnetic

coupling path can be realized by an inductive element. Us-

ing this method can be more intuitive to reflect the main

spatial distribution of the electric and magnetic coupling

paths, so it offers the advantages of easy design, simple

analysis, and flexible control of TZs and loading effect for

size reduction. Equivalent electric and magnetic coupling

separation path theory is based on preset indicators, such as

the position of TZs, return loss, out-of-band rejection, and

other information, to determine the structure of the filter.

This approach is also divided into two methods: the first is

to optimize the circuit directly based on the coupling ma-

trix, and the second is to synthesize it in the low-pass do-

main and then convert it to the bandpass domain. That first

approach relies on the cost function, and the second relies

on rotating and scaling the transformation of the low-pass

prototype. For example, we can introduce the separating

electric and magnetic coupling path regulation theory in the

commonly used cascaded triplet (CT), cascaded quadruplet



Suspended slot line

Air cavity

Multiple inner layers

Waveguide mode

Air cavity

Substrate Metal

Cavities with embedded medium

Dielectric block

Air cavity

Suspended CPW

Metasubstrate

Composite metasubstrate

Via holes

Cut out

(c)

Figure1The concept of three methods of regulating and controlling of electromagnetic field in circuits. (a) SEMCP topology and its applications [1];

(b) The regulation and control of electromagnetic energy storage in coupling [2]; (c) The regulation of electromagnetic field in the metasubstrate or air

cavity [12], [13]. (continued)



Regulation and Control of Electromagnetic Field in Radio-Frequency Circuits and Systems 0030101-3

ELECTROMAGNETIC SCIENCE

(CQ), and other cascade topologies to generate more TZs,

thus effectively improving the filter selectivity.

2. Theory and applications in filters

As a promising method to produce flexible TZs, we have

studied the underlying synthesis theory and then implement-

ed SEMCP in various circuits. As an example, Figure 2(a)

shows a second-order microstrip bandpass filter using the

fundamental SEMCP block, which offers two independent-

ly controlled electric and magnetic coupling paths. The re-

lationship between the coupling coefficients, electrical cou-

pling, and magnetic coupling can be established using even-

odd modes analysis, and the coupling between the two

modes can be described by a separate coupling parameter

, as shown in equation (1).



C =

−ω

+ ω

= F(Y

−C

) = M −E (1)

where



F =

4(A + Y

+ Z

)

(2Y

+ A)

+ (2Z

+ A)

(2)



A =

√

(

+ l

)

(3)



M = FY

(4)



E = FZ

(5)



√

(6)

where

is the propagation constant at the even-mode reso-

nance angular frequency



A′

I/O port

I/O portI/O port

I/O port

CouplingResonator

E: Electrical coupling M: Magnetic coupling

1 2

(a)

(b)



Figure2Proposed second-order filter configuration and the topology.

(a) Configuration with lump coupling elements; (b) Filter topology [1].



The even-mode resonant angular frequency can be giv-

en by



2(2L

+ A)

(7)

The odd-mode resonant angular frequency can be de-

termined by



2(2C

+ A)

(8)

= 1/Y

+ l

≈ λ

where and are lumped elements. We can observe that

the coupling coefficients of the proposed SEMCP are devel-

oped by two separate parts, i.e., magnetic coupling

and

electric coupling

, and the two coupling paths are depen-

dent on one another and have canceling effects.

denotes

the speed of light in free space, and is the charac-

teristic impedance of the resonator. For a small or ,

Figure 2(b) shows the responses of the presented sec-

ond-order BPF using SEMCP. As shown, by selecting a dif-

ferent dominant coupling path and coupling element values,

the filter response could be totally regulated. The design of

narrow bandwidth BPFs requires a reduced coupling coeffi-

cient, which can benefit from the canceling effects in two

coupling paths. Numerous excellent works on electromag-

netic regulation of planar circuits by separating electric and

magnetic coupling paths have been presented and have

achieved favorable performance in terms of compact size,

low losses, etc. In [1], the concept of the SEMCP and the

topology (shown in Figure 2) was proposed, and the cou-

pling mechanism was analyzed based on the equivalent

electric and magnetic path separation.

= 0

Figure 3(a) illustrates the impact of the coupling ele-

ments ( and ) in the two coupling paths on the filter

when magnetic coupling is prominent. When , there

is just one TZ produced in the high stopband as a result of

the harmonic effects. When is greater than 0, a second

TZ is produced in the high stopband, and the filter exhibits

excellent roll-off in this region.



Frequency (GHz)

| (dB)

0.5

(a)

(b)

−80

1.0

=0.3 nH, C

=0.05 pF

=12.5 mm

=1.5 mm

=50 Ω

=0.15 nH, C

=0 pF

=0.15 nH, C

=0.01 pF

1.5 2.0 2.5 3.0 3.5

−60

−40

−20

Frequency (GHz)

| (dB)

0.5

−80

1.0

=0.1 nH, C

=0.1 pF

=12.5 mm

=1.5 mm

=50 Ω

=0 nH, C

=0.05 pF

=0.05 nH, C

=0.05 pF

1.5 2.0 2.5 3.0 3.5

−60

−40

−20



Figure3

spectrum responses of SEMCP filters. (a)

dominant; (b)

dominant [1].



Figure 3(b) shows how the coupling elements ( and

) in the two coupling paths affect filter performance

0030101-4 Electromagnetic Science, vol.1, no.3

ELECTROMAGNETIC SCIENCE

= 0

> 0

when the electrical coupling is significant. No finite TZ val-

ue may be formed in the stopband when . Two more

TZs are produced in the stopband when , and the fil-

ter exhibits a nice roll-off.

To physically implement the SEMCP, we propose

three second-order filter structures based on physical path

separation (shown in Figure 4). These designs use a modi-

fied quarter-wavelength resonator with a coupling gap or

coupled transmission line to achieve the lumped capaci-

tance and use either a via-hole or a short section of a high

characteristic impedance transmission line grounded

through a series-connected via-hole to achieve the lumped

inductance.



(a) (b) (c)

Via

Tap Tap

Tap



Figure4The SEMCP filters. (a) Structure 1; (b) Structure 2; (c) Struc-

ture 3 [1].



In such systems, the electric coupling is prominent.

The electric and magnetic coupling cancel each other out in

the operational frequency range when the external quality

factor is known. As a result, the operating frequency falls

due to the increasing load on both coupling routes, while

the filter bandwidth, which is mostly influenced by the in-

terstage coupling coefficient

, varies minimally. Figure

5(b) illustrates the situation where magnetic coupling domi-

nates. Because of the canceling effect of the two coupling

paths, the coupling of each path increases, resulting in a

lower operating frequency. As a result, the filter’s band-

width can remain almost unchanged even with increased

electrical and magnetic coupling.

Additionally, Figure 6 uses the SEMCP structure to

depict the th-order SEMCP filter topology. Its novelty is

that every pair of neighboring resonators in the filter has ac-

cess to two quasi-independent, controllable

and

cou-

pling paths. Figure 7(a) illustrates how the dominant mag-

netic coupling can be exploited to generate TZs in the up-



Frequency (GHz)

| (dB)

1.0

(a)

−40

1.4

Fig. 4(a)

Fig. 4(b)

Fig. 4(c)

=3.2 mm, R

via

=0.1 mm

=1.7 mm, R

via

=0.3 mm

1.8 2.6 3.4 4.62.2 3.0 3.8 4.2 5.0

−30

−20

−10

Frequency (GHz)

| (dB)

1.0

(b)

−50

1.3

Fig. 4(a)

Fig. 4(b)

Fig. 4(c)

1.9 2.2 2.81.6 2.5 3.0

−40

−30

−20

−10

Figure5Frequency responses of the SEMCP filters. (a)

dominant;

(b)

dominant [1].



Source

0,1

1,2

Load

n−1 n

2,3

j,j+1

n−1,n

n,n+1

Figure6Topology of the high-order SEMCP filter [1].



Frequency (GHz)

Magnitude S

(dB)

(a)

−90

0.3

ii)

Inverted pairs

No-inverted pairs

by M-dominant

by E-dominant

0.6 1.2 1.8 2.70.9 1.5 2.1 2.4 3.0

−70

−50

−30

−10

−20

−40

−60

−80

7.5 mm

8.2 mm

0,1

1,2

2,3

j,j+1

n,n+1

n−1,n

Load

n−1

Source

Tap

Via

(b)

(c)

(d)

Figure7The fourth-order SEMCP filter. (a) Simulation; (b) Configura-

tion; (c) Topology; (d) Comparison photographs with hairpin filter [1].



Regulation and Control of Electromagnetic Field in Radio-Frequency Circuits and Systems 0030101-5

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