Introduction

Radio-Frequency Integrated Circuits

1 Introduction

Introduction

Important

All course material (source code of this document, Jupyter notebooks for calculations, Xschem circuits, etc.) is made publicly available on GitHub (follow this link) and shared under the Apache-2.0 license.

Please feel free to submit pull requests to fix typos or add content! If you want to discuss something that is not clear, please open an issue.

This is the material for an introductory radio-frequency integrated circuits course. The contents are largely based on (Razavi 2011; Darabi 2020); these two books are an excellent introduction to this topic and are highly recommended! For a general introduction to RF and microwave, (Pozar 2011) is a great read!

It is assumed that readers are familiar with the contents of this Analog Circuit Design course.

The production of this document would be impossible without these (and many more) great open-source software products: VS Code, Quarto, Pandoc, LaTeX, Typst, Jupyter Notebook, Python, Xschem, ngspice, CACE, pygmid, schemdraw, Numpy, Scipy, Matplotlib, Pandas, Git, Docker, Ubuntu, GNU/Linux, …

1.1 Wireless Transmission

Wireless Transmission

Figure 1: The block diagram of a simple wireless system.

In wireless transmission, we usually want to transmit data from a transmitter (TX) and its connected antenna towards a receiver (RX) using an electromagnetic (EM) wave. This arrangement is shown in Figure 1.

Wireless Transmission

• The wireless channel is shared between all users.
• As a consequence, the available bandwidth is shared; this means that bandwidth is a scarce resource.
• The wireless channel has significant losses.
• The channel is time variant, as usually the transmitter and/or the receiver move, and/or the environment changes.

Unfortunately, wireless transmission is hard. The wireless channel, i.e., the usage of electromagnetic waves to transmit information from a transmitter to a receiver, while tremendously useful, has quite a few undesired features:

In order to estimate the received power \(P_\mathrm{R}\) from a wireless transmission, we can use Friis’ transmission formula (Pozar 2011):

Wireless Transmission

\[ P_\mathrm{R} = \frac{P_\mathrm{T} \cdot G_\mathrm{T}}{4 \pi d^2} \cdot A_\mathrm{R} = P_\mathrm{T} \cdot \frac{A_\mathrm{R} \cdot A_\mathrm{T}}{d^2 \lambda^2} \tag{1}\]

\[ G = \frac{4 \pi A}{\lambda^2}, \tag{2}\]

Here, \(A_\mathrm{R}\)/\(A_\mathrm{T}\) is the effective area of the receive/transmit antenna, while \(d\) is the distance (line of sight) between the two antennas, and \(\lambda\) is the wavelength of the EM wave. The first form of Equation 1 is simply the power density at distance \(d\) (the transmit power spread over a sphere, boosted by the transmit antenna gain \(G_\mathrm{T}\)) multiplied by the effective area of the receive antenna. The second form follows by substituting the general relation between antenna gain and effective area,

for the transmit antenna. The effective area of an antenna depends on the type and construction, but generally we can say that

Wireless Transmission

\[ A \propto \lambda^2 \]

\[ c = \lambda f. \]

For an isotropic antenna (a theoretical construct where the radiation is of equal strength in all directions) \(A = \lambda^2 / (4 \pi)\), while for a \(\lambda/2\)-dipole \(A = 0.13 \lambda^2\). Of course, the speed of light \(c = 3 \times 10^{8}\,\text{m/s}\) relates frequency \(f\) and the wavelength \(\lambda\) of an electromagnetic wave by

Generally speaking, the size of an electromagnetic antenna is proportional to the wavelength of the EM wave used for transmission. For many devices, we seek antennas with dimensions on the order of a few centimeters, and this is why frequencies in the hundreds of MHz to GHz are so popular. Table 1 lists a few typical applications and their frequencies and wavelengths.

Wireless Transmission

Table 1: Typical RF applications with their operating frequencies and corresponding wavelengths

Application	Frequency	Wavelength
FM Radio	88 MHz to 108 MHz	3.4 m down to 2.8 m
WiFi (lowband)	2.4 GHz	12.5 cm
WiFi (highband)	5 GHz	6 cm
Bluetooth	2.4 GHz	12.5 cm
Cellular	0.6 GHz to 5 GHz	50 cm down to 6 cm
GNSS	1.575 GHz	19 cm

As you can see in Table 1, many of these antennas would not fit into typical device form factors, i.e., often we have to use electrically small antennas. As antenna design is not part of this course but critically important for wireless systems, please refer to (Balanis 2005) or this website for more information on antenna design.

Wireless Transmission

Note 1: Wavelength Calculation

Let’s calculate the wavelength for a Bluetooth signal at 2.4 GHz. Given:

• Frequency \(f = 2.4\,\text{GHz} = 2.4 \times 10^9\,\text{Hz}\)
  
• Speed of light \(c = 3 \times 10^8\,\text{m/s}\)

Using the relationship \(c = \lambda f\), we can solve for wavelength:

\[\lambda = \frac{c}{f} = \frac{3 \times 10^8\,\text{m/s}}{2.4 \times 10^9\,\text{Hz}} = 0.125\,\text{m} = 12.5\,\text{cm}\]

This means that a quarter-wavelength monopole antenna for 2.4 GHz Bluetooth would be approximately 3.1 cm long, which easily fits into most mobile devices.

Wireless Transmission

\[ P|_\text{dBm} = 10 \cdot \log_{10} \left( \frac{P|_\text{W}}{1\,\text{mW}} \right) \tag{3}\]

In order to get a feeling for the attenuation experienced in wireless communication, we now calculate the following example transmission. We will use the unit of dBm which is often used in RF design and is defined as

which is a logarithmic measure of power relative to 1 milliwatt. For example, 1 W = 30 dBm, 100 mW = 20 dBm, and 1 mW = 0 dBm.

Wireless Transmission

Note 2: Wireless Transmission

We use the following parameters:

• Transmit power \(P_\mathrm{T} = 1\,\text{W}\)
• Frequency \(f = 2.4\,\text{GHz}\)
• Communication distance \(d = 10\,\text{km}\)
• Using \(\lambda/2\) dipoles on both ends

Using Equation 1 we calculate

\[ P_\mathrm{R} = P_\mathrm{T} \cdot \frac{0.13 \lambda^2 \cdot 0.13 \lambda^2}{d^2 \lambda^2} = P_\mathrm{T} \cdot 0.13^2 \left( \frac{\lambda}{d} \right)^2 = 2.64\,\text{pW} = -85.8\,\text{dBm} \]

With the transmit power of 1 W = 30 dBm we have an attenuation of 116 dB! This is a very large number!

Wireless Transmission

\[ \text{FSPL} = 20 \cdot \log_{10}(d / \text{m}) + 20 \cdot \log_{10}(f / \text{Hz}) + 20 \cdot \log_{10} \left( \frac{4\pi}{c} \text{m/s} \right). \tag{4}\]

The loss we calculated in Note 2 is called the free-space path loss (FSPL). It is the minimum loss we can expect in a wireless communication system. In reality, the situation is often even worse. The FSPL (in dB) can be calculated as

Equation 4 can be readily derived from Equation 1 and Equation 3 assuming isotropic antennas at transmitter and receiver. Using Equation 4 we can calculate the FSPL for different distances \(d\) and frequencies \(f\). The results are shown in Figure 2. It should be noted that the FSPL increases by 20 dB per decade of distance and 20 dB per decade of frequency, making the use of higher frequencies and longer distances very challenging.

Wireless Transmission

Figure 2: Free space path loss vs. distance for different frequencies (1 GHz, 10 GHz, and 100 GHz).

Wireless Transmission

• The given attenuation is for line-of-sight paths; often, the attenuation is significantly higher than this due to blockage by buildings, mountains, rain, or foliage.
• In the absence of a direct line-of-sight path, the EM wave is redirected by reflections, causing additional attenuation and potential destructive interference due to multi-path reception.

As dire as the situation of Figure 2 already looks, these are not even all the factors to consider:

The consequences of this are (among others):

• The transmitter needs to generate enough transmit power to overcome the transmission loss; this has to be done with high efficiency, as the transmit device is battery operated or limited by cooling.
• The receiver has to be able to process weak signals, i.e., the noise level of the signal processing has to be very low.
• Often, the receive signal is very weak, while there are strong signals at other frequencies (i.e., other wireless transmitters are located close to the receiver). This means the receiver has to be able to process a weak signal while simultaneously tolerating large interfering signals (called blockers).
• Since the frequency spectrum is shared among many users and wireless applications, the transmit information has to be packed efficiently into a small bandwidth.
• Very often, wireless devices are battery-operated. This means transmit and receive functions have to be implemented using minimum power consumption.

Wireless Transmission

• TX: enough transmit power at high efficiency
• RX: process weak signals with low noise
• RX: tolerate large interfering signals (blockers)
• Pack information into a small bandwidth
• Battery operation: minimum power consumption

1.2 Wireless Standards

As stated in the beginning, designing wireless systems is hard.

Wireless Standards

Table 2: Comparison of wireless communication standards

Standard	GSM (2G)	WCDMA (3G)	LTE (4G) 5G NR	WiFi	Bluetooth	GNSS
Frequency range (MHz)	850, 900, 1800, 1900	850, 900, 1700, 1900, 2100	Multiple bands 450…7100 (FR1), 24000…48000 (FR2)	2400, 5000, 6000	2400	1500, 1200
Modulation	GMSK, 8PSK (EDGE)	QPSK (DL), BPSK (UL), 16QAM (HSPA), 64QAM (HSPA)	QPSK, 16QAM, 64QAM (DL+UL) 256QAM (DL+UL)	BPSK, QPSK, 16QAM, 64QAM, 256QAM, 1024QAM, 4096QAM	GFSK (m=0.28…0.35), \(\pi\)/4-DQPSK, 8DPSK	BPSK, QPSK
Transmission/ multiple access	TDMA, FDMA	DS-CDMA	OFDMA (DL+UL), SC-FDMA/DFT-s-OFDM (UL)	OFDM, CSMA/CA	FHSS	CDMA
Duplex	FDD	FDD	FDD, TDD	TDD	TDD	n/a

In order to allow communication between different devices, different operators, and different manufacturers, wireless communication is usually standardized. There are many different standards, each with its own characteristics. Wireless standards define every aspect of wireless communication, and can be documents of hundreds or thousands of pages. Here, we mainly focus on the radio-frequency and analog aspects of wireless standards. Summarized in Table 2 are a few popular wireless standards with their main characteristics.

Wireless Standards

Standard	GSM (2G)	WCDMA (3G)	LTE (4G) 5G NR	WiFi	Bluetooth	GNSS
Channel bandwidth	200 kHz	5 MHz	1.4, 3, 5, 10, 15, 20, …, 100 MHz (FR1), 400 MHz (FR2)	10, 20, 40, 80, 160, 320 MHz	1 MHz	16…24 MHz
Symbol rate1	270.833 ksym/s	3.84 Msym/s	15/30/60 ksym/s	312.5 ksym/s (11a/g/n/ac), 78.125 ksym/s (11ax/be)	1 Msym/s	50 sym/s
Pulse shaping	Gaussian (BT=0.3)	Root Raised Cosine (\(\alpha\)=0.22)	Rectangular	Rectangular	Gaussian (BT=0.5)	Rectangular

1. For the OFDM-based standards (LTE/5G NR, WiFi), the listed values correspond to the subcarrier spacing (numerology \(\Delta f\)), which equals the per-subcarrier symbol rate; they are not the aggregate symbol rate of the full signal.

Wireless Standards

Standard	GSM (2G)	WCDMA (3G)	LTE (4G) 5G NR	WiFi	Bluetooth	GNSS
Transmit power	1…2 W	250 mW	200 mW (FDD), 400 mW (TDD)	100 mW	1…100 mW	n/a
PAR (UL)	0 dB (GMSK), 3 dB (8PSK)	3…8 dB	6…8 dB	Up to 12 dB	0 dB (GFSK), 3 dB (8DPSK)	n/a
MIMO	no	Not realized (DL 2x2)	DL 4x4 (up to 8x8)	2x2 (up to 8x8)	no	no
Channel bond	no	Up to 4x5 MHz	Up to 7x20/4x100 MHz	Up to 80+80+80+80 MHz	no	no

During this course, we will learn what these terms mean and how they impact the design of RF integrated circuits.

As you can see in Table 2, since LTE (4G) and 5G NR, many additional bands have been defined in the sub-6 GHz range (FR1) and also in the mm-wave range (FR2, 24.25 to 52.6 GHz). This means that modern wireless devices have to support many different frequency bands, which makes the design of RF front ends even more challenging. A good overview of the different frequency bands is given here for LTE and 5G NR.

RFIC design is a multidisciplinary field, requiring knowledge from various engineering domains, as shown in Figure 3. This makes RFIC design challenging, but also very interesting!

Wireless Standards

Figure 3: RF design as a multidisciplinary field requiring knowledge from various engineering domains (adapted from (Razavi 2011)).

Wireless Standards

Figure 4: RFICs require careful design considerations and trade-offs (adapted from (Razavi 2011)).

Further, RFIC design requires careful consideration of many different aspects, as shown in Figure 4. Many parameters are often tightly coupled, requiring careful trade-offs during the design process.

References

Balanis, Constantine A. 2005. Antenna Theory: Analysis and Design. Wiley-Interscience.

Darabi, Hooman. 2020. Radio Frequency Integrated Circuits and Systems. 2nd edition. Cambridge University Press.

Pozar, David M. 2011. Microwave Engineering. 4th edition. Wiley.

Razavi, Behzad. 2011. RF Microelectronics. 2nd edition. Pearson.

References