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Welcome to Tim’s Blackboard! This is the place to find discussions on interesting topics related to signal integrity and power integrity.


This week on Tim’s Blackboard, convolution workspace!

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At the bottom of the page, there are links to the available workspaces.

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Use ADS to unarchive the workspaces:

         For engineering students and professionals alike, ADS simulations are a dream come true. A software that does all the calculations for me? Count me in!


         As today’s circuits grow more and more complex, the processes involved in creating, testing, and simulating them tend to follow suit. RF engineers face many challenges in RF design. With vast applications and flourishing technology, engineers need an efficient, easy-to-use workspace to construct their innovative creations.


         In his webcast, RF Simulations Basics, Andy Howard, Senior Applications Engineer and EEsof Applications Expert for 30 years, guides us through the basics of RF Simulation in ADS, showing how it is a valuable tool with multiple applications. For those just getting introduced to RF simulations, this webcast is a great resource for understanding how to perform RF simulations and why. Andy provides six prevalent applications for RF Simulations, two of which I will discuss here, that show us why ADS is the integral part in bringing engineering ideas to life.



Figure 1: ADS helps RF engineers bring their ideas to fruition with its efficient, easy-to-use RF simulation guides.



RF Simulations with ADS

ADS offers a comprehensive set of advanced simulation tools, integrated into a single environment. In the webcast, Andy gives you a feel for what it’s like to run the ADS software. He shows how an ADS user can design a simple block diagram using models. These models represent transmission lines, transistors, capacitors, etc. These are “the building blocks of effective simulations.” Simulating S-Parameters of your RF design is similar to using a network analyzer; however, with ADS you can combine multiple blocks with several different parameters. There is no limit to the number of ports.


The interface allows you to adjust the parameters of each component as you place it in your schematic and set frequency limits. When the design is complete, Andy shows how you can view the Data Display window and tune the component values simultaneously. This provides an excellent visualization of how your design truly depends on the different component values.



Figure 2. With ADS, users can view the Data Display window and tune the component values simultaneously.


What can be achieved with RF Simulation?


1. Better receiver performance for all your communication devices.

The applications of ADS are vast. A simple example Andy gives is an FM Radio Receiver. The simulation provides data at each node of the block diagram, allowing him to determine precisely where the receiver has performance degradation. He also views a spectrum of a particular node, which can indicate spectral content. By doing this example in ADS, the designer can more quickly see which components are causing the degradation.  The engineer can make more accurate predictions about their design without having to do many messy calculations. ADS also allows you to tune the parameters of your devices within the block diagram, allowing you to make adjustments as needed. 



Figure 3: The simulation of an FM Radio Receiver provides data at each node of the block diagram, allowing one to determine the precise location of performance degradation. Simulation done by ADS.




2. Integration of Multiple Technologies

The coupling of multiple technologies is a challenge often faced by RF designers, especially now as multi-tech devices are becoming more common place. Therefore, the need for compatibility between the technologies is imperative. For example, many companies use ADS to design parts such as a Multi-Chip RF Front End Module, as it is popularly used to power smart phones and tablets. ADS allows designers to take a pre-existing module, and virtually mount it on a board. Using multiple technologies can often cause performance degradation and increased simulation times. ADS is unique in its ability to ensure compatibility between different modules and technologies.



Figure 4. ADS allows designers to take a pre-existing module and virtually mount it on a board, allowing RF designers to couple multiple technologies into one simulation. Simulation done by ADS.


         These are only two of many applications of RF Simulations through ADS. Andy provides insight into these as well as four other applications of RF Simulations, including Electro-Thermal Analysis and High Speed Digital Design. He also delves into the different types of simulation engines which allow you to analyze your design’s harmonic balance results and transient simulations.

         Andy has over 15 years of experience designing and simulating circuits. For those looking for an introduction to the fundamentals of RF simulations, Andy provides a well-structured one-hour lecture that describes the multiple uses of RF design software. With these fundamentals, RF students and professionals can easily make their ideas into a reality.   




Welcome to Tim’s Blackboard! This is the place to find discussions on interesting topics related to signal integrity and power integrity.


This week on Tim’s Blackboard is “Convolution and Single Pulse Response.”



Two weeks ago, in the “Dirac Delta Misnomer” post, I explained why Dirac delta function is technically a distribution. I also talked about the impulse response: the response of a system given the Dirac delta distribution as the input.


This week, I will demonstrate the concept of convolution and the process of generating single pulse response using convolution, as shown in Fig. 1.

Fig. 1: ADS simulation result of the single pulse response generated by old-school convolution.


System Level Abstraction

Before delving into the concept of convolution, I want to first show the top-level system diagram to place the impulse response in context.


In Fig. 2, you can see the input goes into the channel and out comes the output at the…… output. In general, we don’t know how the channel operates because we do not have the information for the channel behavior , which is the reason for the question marks.  


Fig. 2: By injecting an impulse at the input of the channel, one obtains the impulse response of the channel under test. Because the impulse response completely characterizes a system, one now knows the channel behavior.


To obtain a behavioral model for the channel, one sends an impulse (Dirac delta distribution) at the input of the channel. Because the impulse response completely characterizes the channel, the channel response at the output is the behavioral model of the channel we are looking for. (To learn more about signal and systems, I strongly suggest 6.003 from MIT open courseware.)      


The Concept of Convolution

The form of the expression,


shows up naturally in the solution of differential equations by integral transforms (like Fourier or Laplace transforms) related to electrical engineering, optics, probability and statistics, and other disciplines [1].


In the context of the linear time-invariant (LTI) systems, such as a high-speed channel, once we have the impulse response of the channel, the output of the system is the convolution of the input and the channel behavior, see Fig. 3.      

Fig. 3: The convolution operation appears when one computes the output of a channel, where the channel has impulse response, h(t), and x(t) at the input.  


If we expand the short hand notation, , we arrive at the familiar form


Graphical Convolution in Action

It’s hard to make out what is happening from the classic convolution integral, so I will represent the equation graphically.

Say we have a function, , shown in Fig. 4, and we want to calculate the convolution of the function with itself.  


Fig. 4: Illustration of the function f(t)


To compute the convolution of function with itself, we will flip the function and generate the mirror image, , see Fig. 5.   

Fig. 5: Illustration of f(-t), the mirror image of the function f(t)


Finally, we slide the mirrored function towards the right. As we slide the mirrored function, we will multiply the two functions and integrate to find the overlapped area. Fig. 6 is the illustration of convolving  with itself at some time t1.


Fig. 6: The shaded region is the value of convolving the two functions at time t1. According to the graph, at time equals to 0.6 units, the result of convolution is 0.6.


In Fig. 6, the shaded area is the value of the convolution at time t1, to find out convolution results for all time, we will keep sliding, increasing time and calculate the overlapped area at each time step. We can expect that as we slide the pink rectangle to the right, we will reach a maximum overlapped area at time equals to 1 unit, where the two rectangles are right on top of each other. Afterwards, we expect the area to start decreasing to zero.


The result of the convolution is shown by the red curve in Fig. 7. The red dot shows the value of the product of the two functions integrated throughout the entire time axis at a specific time t. The red trace left behind the red dot is the convolution result for all time.  


Fig. 7: Animation of convolving a rectangular function with itself. The red curve shows the result of the convolution. Fun Fact: convolving two rectangles gives you a triangle.


Generating Single Pulse Response

The single pulse response of a channel is the result of convolving a single pulse with the impulse response of the channel. In this example, the single pulse comes from a 10 Gbps transmitter and has a duration 0.1 nsec, shown in Fig. 8.

Fig. 8: The setup for single pulse response convolution.


Like the rectangle example, to get the single pulse response, we slide the single pulse, find the overlapped area by multiplication and integration. Similarly, we would expect the single pulse response to increase and reach a maximum value and decrease to zero. Note the single pulse response has voltage range from 0 to 1 V, the result of multiplying a large voltage value in GV scale with a small time value in nsec scale.


Shown in Fig. 9, the result from the simulation agrees with our expectation and we now have the knowledge of the response of the channel to a 10 Gbps pulse.  


Fig. 9: ADS simulation of single pulse response computed with convolution.


The Story Told by a Single Pulse  

You might be thinking, “Why do we care about the single pulse response?”


The short answer: because we can learn a lot from the signature of the waveform, especially when equalization is used at the transmitter and/or receiver. Interested readers can find more information in the attached single pulse response slides I presented in DesignCon 2017.


Convolution is quite a revolutionary concept in dealing with signals and systems in the time domain. In the coming weeks, we will start moving toward the frequency domain and become “bilingual” in both time and frequency domain.


I am working on putting together a workspace for this post and it should be up next week in TB #3.5. 


That's this week's Tim's Blackboard. See you in two weeks!


To download ADS so you can learn more about convolution:


[1] A. Dominguez. (2015, Jan. 24). A History of the Convolution Operation [Online]. Available:  


Understanding the impact thermal effects can have on your circuit design is critical to being able to adequately account for them during the design process. It’s also essential to designing your circuit in an efficient way. But that’s easier said than done. A recently released video from Wolfspeed may offer you some much-needed help.


The solution involves using the Wolfspeed MMIC process design kit (PDK) that works in Keysight EEsof EDA’s Advanced Design System (ADS) software. A key feature of the Wolfspeed ADS MMIC PDK is that it’s configured to work with the ADS Electro-Thermal Simulator to co-simulate electrical and thermal performance. The feature is a powerful tool that allows you to account for the significant thermal effects that can occur when using a high-power density technology like GaN.

To demonstrate this capability, the video details the example of a simple, single-pole tuned 10-GHz power amplifier. The design uses a 1.2-mm FET and its goal is to put out about 5 watts at temperature.

Layout of the single-pole tuned 10-GHz power amplifier, designed using only elements from the PDK itself.

The layout of the single-pole tuned 10-GHz power amplifier, designed using only elements from the PDK itself.


 Schematic of the electro-thermal simulation of the single-pole tuned 10-GHz power amplifier.

Schematic of the electro-thermal simulation of the single-pole tuned 10-GHz power amplifier.


Data display of the simulation of the single-pole tuned 10-GHz power amplifier from Keysight ADS software.

Data display of the simulation of the single-pole tuned 10-GHz power amplifier from Keysight ADS software.


With the ADS Electro-Thermal Simulator, Wolfspeed was able to get an accurate, “temperature aware” IC simulation result for the PA using device temperatures that took into account both thermal coupling and the thermal characteristics of the package.

Electro-thermal simulation of the single-pole tuned 10-GHz power amplifier. Peak is at 180 degrees.

 Electro-thermal simulation of the single-pole tuned 10-GHz power amplifier. The peak is at 180 degrees.


3D view of the electro-thermal simulation of the single-pole tuned 10-GHz power amplifier.

3D view of the electro-thermal simulation of the single-pole tuned 10-GHz power amplifier.


For specific details on how the ADS Electro-Thermal simulator was used in the design of the 10-GHz PA, watch the video below.


More information on the ADS Electro-Thermal Simulator is available here.


free trial, ADS, Keysight

Welcome to Tim’s Blackboard! This is the place to find discussions on interesting topics related to signal integrity and power integrity.


This week on Tim’s Blackboard, I will resolve the arrival time inconsistency shown in the previous post.  



Last week, we sent an impulse through a section of 50-Ohm, 6-inch microstrip transmission line and expected the impulse to arrive at 1 nsec. However, the impulse arrived 0.88 nsec at the output, see Fig. 1.


Fig. 1: ADS simulation result from last week's post. We expected the impulse to reach the output at 1 nsec, but the impulse arrived at 0.88 nsec.


Assumption, Assumption, Assumption

The answer to our question is in the assumption we made when we were calculating the time delay. The rule of thumb for the speed of propagation, 6 inch/nsec, assumes the Dk (dielectric constant) to be 4.


The speed of light in vacuum is 3*108 m/sec, or 30 cm/nsec, and alternatively, about 12 inch/nsec. To calculate the speed of propagation in a different medium, we divide the speed of light in vacuum by the square root of Dk: 



  Given an FR4 substrate with Dk = 4, the speed of propagation is:




Microstrip and Effective Dk

The Dk of FR4 is indeed 4, but that's not the whole story. When a signal propagates in a microstrip environment, it sees both FR4 and air. The result of the signal interacting with both medium is a lower effective DK.


A lower effective Dk would increase the propagation speed and lower the delay: consistent with last week’s result.

Having a guess of what was happening, we proceed to verify whether our guess is correct.


Consistency Test

Since the possible root cause of the early arrive time is the lower Dk due to air, we need to ensure the signal only sees the Dk of FR4. To do so, we place the same transmission line in a stripline environment, where the trace is only surrounded by FR4 material.  


Fig. 2: The same 6-inch transmission line with 20 mil trace width. Note the height of the substrate is changed so the impedance of the line is still 50 Ohms.


To make sure we are doing an apples-to-apples comparison, the substrate height is increased so the impedance of the transmission is still 50 Ohms, see Fig. 2.


We then perform the identical simulation with the new substrate. Shown in Fig.3, the result of the impulse indeed arrives at 1 nsec, and our guess is now a valid root cause for the shorter delay.

Fig. 3: Signal arrives at the predicted 1 nsec after switching the same 6-inch line into a stripline environment while maintaining impedance of 50 Ohms.

Inconsistency Resolved

Much like the melting trace paradox, our initial assumption was once again inaccurate. However, since we used a rule of thumb to quickly get the numbers for the propagation speed of light in FR4, some degree of inaccuracy could be expected.


As Dr. Eric Bogatin put it, “An okay answer now is better than a good answer later.” As long as we know the underlining assumption in the approximation, it is perfectly fine to use a rule of thumb to quickly estimate the result one is expecting.


That's this week's Tim's Blackboard. See you next week!


Use ADS simulations to perform consistency tests:

Welcome to Tim’s Blackboard! This is the place to find discussions on interesting topics related to signal integrity and power integrity.


This week on Tim’s Blackboard is the “Dirac Delta Misnomer.”



Did you know the famous Dirac delta function is mathematically NOT a function?


Fig. 1: ADS data display representation of the Dirac delta “function” by a line and arrowhead. The tip of the arrow head indicates the multiplicative constant to the Dirac delta. 


The  "function", shown in Fig. 1, can be loosely thought of as a function on the real line which is zero everywhere except at the origin, where it is infinite:


and it is also constrained to satisfy the following identity [1]:


However, there is no function that can simultaneously have all the above properties.
Any extended-real function that is equal to zero everywhere but a single point must have total integral zero [2] [3].


Well, if Diract delta is not a function, what is it?


Dirac Delta Distribution

Mathematically speaking, the Dirac delta “function” is a generalized function or a distribution. It can be considered as the limit of a zero-mean normal distribution when the standard deviation, σ, approaches 0, see Fig. 2.  


Fig. 2: Normal distribution with different standard deviations shown in ADS data display. As the value of standard deviation gets smaller and smaller, the function approaches Dirac delta distribution.


To rigorously capture the notion of the Dirac delta “function”, Mathematicians had also defined a measure. Instead of spending time on the mathematics, we will look at what brings the misnamed Dirac delta distribution to its fame.


Dirac Delta and Impulse Response   

The Dirac delta distribution is well known for many reasons. For example,

1.    The convolution of a Dirac delta function with function F is the original function F, ,

2.    The Fourier Transform of a Dirac delta is unity, , and most importantly,

3.    The response of a given Linear Time-Invariant (LTI) system to a Dirac delta distribution completely characterizes the system.


To build up a good foundation for future discussions on Convolution and Fourier Transform, let’s examine the impulse response: the response of an LTI system to the Dirac delta distribution. (note: in the following sections, the term impulse is used interchangeably with Dirac delta distribution.)  


Impulse Response of a Lossless Channel

Before we bring out simulation tools to simulate the impulse response of a lossless channel, it is important to know what to expect. Dr. Eric Bogatin named the practice Rule #9: “Never perform a measurement or simulation without first anticipating the results you expect to see.”


Shown in Fig. 3 is an illustration of the circuit setup. Given a lossless line with time delay, TD, and no mismatch to create reflection, we will see the impulse at the probe TD seconds after the impulse (Dirac delta distribution) is sent.


Fig. 3: Illustration of sending an impulse through a transmission line with time delay TD seconds  


In this experiment, we used a section of lossless transmission line that is 1 nsec long. Per Rule #9, we should expect the impulse to arrive at the output at 1 nsec.  

ADS Simulation Result  

As shown in Fig. 4, the simulation result is consistent with our expectation. The same impulse indeed shows up at the output 1 nsec after it leaves the source.     


Fig. 4: ADS simulation of an impulse through a 1 nsec long lossless transmission line. As expected, the impulse is delayed by 1 nsec.


Note that because it is impossible to generate an ideal Dirac delta distribution having an infinite amplitude, we are using the arrowhead to denote infinity.In the ADS workspace attached, you will find a method to approximate the impulse. The key is to ensure the approximated Dirac delta distribution has an integral of unity over the entire real line.      

Consistency Test

To make sure our approximated impulse satisfies the constraints formulated before, we also plot the integral of the approximated impulse. We would expect the plot of the integral of the output impulse to be a unit step function starting at 1 nsec.

Fig. 5: The integral of the approximated impulse is indeed the step function we expected.


As shown in Fig. 5, the integral of the approximated impulse fulfills the unit step requirement. We now have confidence in the approximated impulse and the generated impulse response.      


Impulse Response of a Lossy Channel

In real life, a lossless channel does not exist. There is always conductor loss and/or dielectric loss in the transmission line. We will now investigate a 6 inch 50 Ohm microstrip line on an FR4 substrate with a virtual prototype.


Using the rule of thumb, 6 inch/nsec, for the speed of propagation in FR4, we would expect 1 nsec delay for a 6 inch transmission line. In addition, because of the frequency-dependent loss, we would also expect the impulse to spread out. Lastly, we should see a very high voltage peak approximating the infinite amplitude.  

ADS Simulation Setup and Result  

In the lossy case simulation, we used the multilayer layer library substrate and transmission line so a 2D cross-section of the trace is solved by method of moments to gain more accuracy in simulating losses than the equation-based model.

In Fig. 6, the result of the simulation agrees with most of our predictions. The peak of the output voltage is more than 60 GV (daunting) and the impulse is more spread out because of the frequency-dependent loss.


Fig. 6: The result of lossy transmission line simulation agrees with our predictions, except for the arrival time.


Nonetheless, although close to our prediction, the arrival time of the impulse is a bit off. Instead of 1 nsec, the impulse arrives at 0.88 nsec. (Any guesses on why that is? Feel free to post possible explanations in the comment section, and check back next week for the answer.) 


Dirac Delta Misnomer Corrected

After our journey today, we now know that because of its unique definition, the Dirac delta should to refer to as distribution and not a function, a fun fact to bring up at social functions (pun intended).


Moreover, we touched upon the important properties of the Dirac delta distribution. Specifically, the response of an LTI system to a Dirac delta: the impulse response, which characterizes an LTI system completely.  


In future posts, we will build upon the impulse response idea and delve into Convolution and Fourier Transform.

That's this week's Tim's Blackboard. See you in two weeks!


Before then, make sure to download the workspace attached to see how an impulse can be approximated and how the impulse looks like after going through a realistic transmission line!


To download ADS to unarchive the workspace:



[1] Gel'fand, I. M.; Shilov, G. E. (1966–1968), Generalized functions, 1–5, Academic Press

[2] Vladimirov, V. S. (1971), Equations of mathematical physics, Marcel Dekker, ISBN 0-8247-1713-9.

[3] Duistermaat, Hans; Kolk (2010), Distributions: Theory and applications, Springer.


Today we are going to talk about the different types of linear simulation tools ADS provides.  ADS sets up its linear simulations into three different categories:  DC, AC, and S-parameter simulation.  Let’s go over each of these simulations, and how easy they are to run in ADS.


1.  DC Simulation:

Per Ohm’s law(V=IR), you get steady-state DC voltages and currents.  Capacitors are treated as ideal open circuits, and inductors are treated as ideal short circuits.  DC convergence occurs when 2 conditions are met:  Voltage change at each iteration is zero and Kirchoff’s Law is satisfied, meaning the sum of the node currents equal 0. 


 DC Simulation controller & sweep VAR


The DC Simulation icon translates to the following blue image in your workspace.


Once you double-click the VAR eqn icon, you can select the option to sweep, which allows you to sweep a parameter, but it must be declared as a variable.  To declare a variable, or a variable equation, select the following icon:

2.  AC Simulation:

An AC Simulation is performed in the frequency domain.  You can simulate a single frequency point, or across a frequency span in a linear or logarithmic sweep.  


 AC Simulation Controller

The following is what the default settings look like in your workspace. 

AC simulation is either a linear or small signal simulation and the frequency is defined in the controller, not the source.  On-screen parameters can be set in the Display tab.  AC sources are identified as:  V_AC, I_AC, and P_AC.  


3.  S-Parameter Simulation:


S-parameters describe the response of an N-port network to signals to any of the ports you want measurements from in terms of power ratios.  For example, an S12 measurement is the response at port 1 given the input power wave at port 2.      

Results of an S-Parameter Simulation in ADS include:


  • S-matrix with the complex values at each frequency point
  • Gamma value (complex reflection value)

  • Marker readout for Zo (characteristic impedance)
  • Smith chart plots for impedance matching


These results are similar to Network Analyzer measurements, so if you don’t have one, you can simply simulate what you are looking for in ADS.

If you don’t have ADS get a free 30-day trial here.


 S-Parameter Simulation Controller



The link below guides you through examples of an AC and S-Parameter simulation, as a visual walk through experience.


You made a bee line for understanding linear simulations!  The best way to learn is by doing, so check out the attached PDF that will walk you through an amplifier design.  This gives you the chance to see applications of the different types of linear simulations when designing.