Basics

Answer: Frequency, wavelength, and speed of wave are related to each other using the following formula. Note that as frequency increases, wavelength become shorter.

Answer: In the same medium they will travel with the same speed. Both will travel with speed of light in vacuum. In a different medium with a higher dielectric constant both will be slower by a factor of 1/√ε-r. 

Answer: It depends on the type of the TL and also the dielectric constant. For example consider a coaxial line with a dielectric insulating layer (ε-r=4). Wave travels with 0.5 half the speed of light. This is because a coaxial line is a TEM TL with an ε-eff = ε-r. For a different TL with a different ε-eff  than it’s dielectric constant the answer will be different.

Answer: Every RF component/circuitry will have an input impedance that needs to match the impedance of the preceding block. Otherwise there will be an impedance mismatch which results in a high reflection loss. Power coming into the circuit will reflect back. In fact, power delivery is maximum when a conjugate match is present for source and load impedance. In the case of a real impedance such as 50 ohms conjugate match reduces to a simple match for the two impedances. 

Answer: Return loss is the power lost due to reflections occurred because of mismatch between source and load impedances.

Answer: Voltage Standing Wave Ratio is a measure of how well a load is matched to a source. In other words how much of power at the output of the source is delivered to a load connected to the source using a transmission line. For example: how much of the power at the output of an amplifier is delivered to an antenna through a microstrip line.

VSWR is defined using the following formula and is the ratio of the signal on the transmission line:In an ideal system voltage doesn’t change along the TL and thus VSWR is 1 (or 1:1). When mismatch is present in a system voltages vary along the TL and this value will be higher. Based on your experience what different numbers for VSWR mean? Provide some examples.    

Answer: Both return loss and VSWR are indicators of how much reflection is present in a circuit. The following formulas show how these two are related. 

♦ Note how RL and reflection coefficient are related. Even experienced engineers make the mistake of misusing S11 in dB instead of RL. Rule to remember: “Loss is always a positive number!“… (See next question)

Answer: Common mistake: Some people misuse reflection coefficient or the plot for S-11 instead of return loss. In fact return loss and reflection coefficient are the same numbers however they differ in their sign. One is positive and the other is negative (both often expressed in dB). 

Answer: 1 dBm is 10 mw. 1 Watt is 30 dBm. The conversion formulas are listed below. Also memorizing some of the well-known values might become handy for quick calculations.

Answer: Vrms and Vp-p are related using the following formula. When calculating the power Vrms is used. for example in the case of a sinusoidal signal and a 1 dBm power delivered to a 50 ohms load:Note: From previous question we know 1 dBm is 10 mW.

Answer: We usually use linear models that approximately predict how a system acts when operating in small-signal domain. Nonlinearity effects, however, cannot be predicted by the linear models. Main nonlinearity effects that need to be considered when dealing with nonlinear systems are: 

– Harmonic distortion, – Gain compression, – Cross modulation, – Intermodulation

Answer: For a linear device as the power of the input tone increases the output power also increases linearly. For a nonlinear system, however, this is only true when operating in the linear region. Once entering the nonlinear region, the output does not follow the input linearly. There is a point where the output of the system doesn’t increase as much as the input is increased. The point where the gain of the system drops by 1 dB is called the 1 dB compression point and is the parameter widely used to evaluate how a device performs in terms of compression. To boost up this answer you can review all the equations and know how to derive them. 

Answer: Unlike gain compression which is due to a single tone at the input of a nonlinear system, intermodulation happens when two tones appear at the input of a nonlinear system. Based on the nonlinearity type of the system different orders of intermod such as 2nd, 3rd, etc can happen. The most famous ones are the 2nd and 3rd order intermod. The outcome of intermod is extra tones at the input/output of the system. For example the calculation below shows all the tones at the output for the 2nd and 3rd order intermod.  

Answer: Third intercept point or IP3 is a mathematical approximation that relates the products generated by third order nonlinearities to the amplified linear term. This concept can be calculated for both input and output which results in IIP3 and OIP3. Below figure shows how IP3 is found and also an approximation method to calculate IIP3 based on the input tone power level and output measured signals. Keep in mind that IIP3 is just a mathematical concept that helps us compare different devices and see how nonlinear they are. Most of the time, 3rd intercept point happens beyond the damage threshold of RF components. Thus it does not relate to a practical measurable power level. 

Answer: There are different levels of how this can be answered. Based on the knowledge of the interviewee the response varies. As this is the basics page of RF QAs, only a very simple setup will be shown here. However, reader is encouraged to read the answers to the same question in the intermediate and advanced sections as well. 

For a two tone test, as simple as it sounds we need two sources, a combiner to combine the two tones, and a spectrum analyzer to monitor the two tones. This will be the most basic answer one can give. Based on whether the device under test is a one port or a two port device the system can change. For a one port device we can do a reflective measurement. And for a two port device, depending on reciprocity, both reflective or thru measurements can be used. Figure below shows a two-port IMD3 measurement system. How would the system look like for a one-port device? (IMD measurements is a tough experiment which requires experienced microwave engineers. The lower the level of IMD tones, the harder the measurement becomes. Engineers are encouraged to master this measurement as usually at least of the interviewers focuses on this setup.)  

Looking at this setup, could you answer:

Why two PAs are used?

Why to use circulators?

What are the challenges with this system? 

How would you improve this setup? 

Answer: From previous questions we know the formulas for A(in,1dB) and A(in,IIP3). Thus:This is showing that A(in,IIP3) is almost 10 dB higher than A(in,1dB). Meaning that as we increase the input power P1dB happens faster in a nonlinear device. Then why do we even care about PIIP3? If you cannot answer this question, go back to the IIP3 question and read again the answer to what is IIP3 and how can it be estimated. 

Answer: Total IIP3 of a cascade system (such as a receiver chain) can be calculated from the following:

where, α and β are gain for first and second stages, respectively. AIIP3,n is representing the IIP3 of each block.

The important takeaway from this formula is that the IIP3 of the latter stages becomes increasingly more important as IIP3 of each stage is scaled by the gain of all previous stages. Of course this is only true as long as all stages have a gain number greater than unity.

Do you know any kind of stage that is not like that? What will be the effect of such stages then? 

Answer: White noise occupies the entire frequency spectrum. Low pass filters will only pass a portion of this noise in the system and will dampen the rest at higher frequencies based on the rejection level. The same applies to bandpass filters. They will reduce the PSD based on their BW and rejection level. Now that we know this, how can we relate it to how a spectrum analyzer works? 

Answer: SNR is a measure used to compare the level of a desired signal to the level of background noise. Defined as the ratio of signal power to noise power. SNR is an important element in RF as it is the base for computing the sensitivity of a receiver. Also, it will be used to define the Dynamic Range (DR), and Spurious-free Dynamic Range (SFDR).

SNR is usually expressed in dB:

Answer: NF is a measure of how a system degrades the SNR. A receiver chain will degrade the SNR based on the components and blocks it incorporates. Lower NF values indicate better performance of the system chain. 

Another definition of NF as Razavi explains in his RF Microelectronics book is as follows: the total noise at the output divided by the noise at the output due to the source impedance.

Another important point is that NF is usually defined for a 1 MHz bandwidth at a specific frequency. Also, note that NF would be always 1 for a noiseless stage. Even if the stage acts as an attenuator. This means that if the stage doesn’t add any noise, then NF equals 1. 

Answer: NF of a lossy stage equals the loss of the system. For example: for a passive circuit, NF will be equal to its insertion loss L = Pin/Pout.

Answer: Total noise figure of a cascaded system can be found using Friis’ famous formula: where NFn is the noise figure of the n-th stage and Gn is the power gain of the n-th stage.

From this formula, it becomes clear that NF of the initial stages in a receiver chain is significantly more important than the latter ones. This is because the NF of each stage is divided by the Gain of all the previous stages. A good way to remember this is to always remember the LNA and why we need it to have such a low NF. 

Answer: Noise presence and other signal corruption mechanisms (ex. fading due to multi-path) causes the receiver to not be able to detect the desired signal all the time. Sensitivity is the minimum signal level that a receiver can detect without losing the intended data. The formula for P-sen is derived from the SNR formula and the fact that SNR-out needs to meet a minimum requirement. As such, the formula for SNR is: 

Considering the receiver is matched to the antenna then P-RS will be equal to KT and thus we will have the following well-known formula for Sensitivity: 

Answer: The level of Noise floor determines the lowest level at which a receiver can receive signals with acceptable BER. For a receiver Noise floor at 20 degC is defined as the first three terms of the Sensitivity formula:

Answer: DR’s simplest definition is as follows:

The difference in dB between the maximum input power level a receiver can tolerate and the minimum it can detect. In RF design and based on different applications DR might have different meanings. Here, we only focus on the simplest form of DR definition. The upper limit is defined by the compression point of a receiver. The level after which the receiver will become excessively nonlinear due to a single tone at the input. This can be quantified as the 1-dB compression point. The lower limit is defined as the sensitivity of the receiver. This type of DR excludes interferes and thus can have a large value. 

Answer: What if the receiver is experiencing two tones at the input. Does the 1-dB compression point still suffice as the upper level for DR definition? This is when Spurious-free Dynamic Range (SFDR) is used. Lower end is still defined by sensitivity of the receiver. Upper end, this time, is defined by the max input level of two tones at which the third-order IM products are smaller than the integrated noise level of the receiver. What else DR definition can you come up with based on an application you have encountered before? 

Answer: A constellation diagram also referred to as the signal constellation is a representation of a digitally modulated signal scheme such as BPSK, QPSK, etc. It displays the signals in a 2-dimensional xy-plane scatter diagram in the complex plane. For constellations for different modulation schemes please see Razavi’s RF Microelectronics book. Interviewees are encouraged to know the differences between these constellations. For example a good question is what is the difference of QPSK and O-QPSK constellations and why? 

Answer: Due to noise, and nonlinear behavior of RF transceivers actual constellation of signal for a system will be different than it’s ideal shape. Error Vector Magnitude (EVM) is a measure of how well the signal quality is. It can be used to understand different effects a system can have on the signal. For example by looking at EVM an engineer can tell whether there is an amplitude compression happening. Or if phase noise issues exist in the system it could be seen in the signal constellation. As such, EVM plays an important role in evaluating the accuracy of an RF system in transmitting symbols. EVM by definition is: 

where er can be defined as the magnitude of each error vector. 

Answer: This is a hard question to summarize an answer for here. Please go over Heterodyne and Homodyne architectures.

You need to be ready to answer questions such as

-) Why did you draw filters before and LNA?

-) Why is the LNA important as one of the very first blocks?

Also be prepared to know the answer to the cons and pros of the architecture you choose. For example a Heterodyne receiver suffers from multiple required filters…