RF Cafe Software

RF Cascade Workbook 2005 - RF Cafe
RF Cascade Workbook

Calculator Workbook
RF Workbench
Smith Chart™ for Visio
Smith Chart™ for Excel
RF & EE Symbols Word
RF Stencils for Visio

About RF Cafe

Kirt Blattenberger - RF Cafe WebmasterCopyright
1996 - 2016
Kirt Blattenberger,

RF Cafe began life in 1996 as "RF Tools" in an AOL screen name web space totaling 2 MB. Its primary purpose was to provide me with ready access to commonly needed formulas and reference material while performing my work as an RF system and circuit design engineer. The Internet was still largely an unknown entity at the time and not much was available in the form of WYSIWYG ...

All trademarks, copyrights, patents, and other rights of ownership to images and text used on the RF Cafe website are hereby acknowledged.

My Hobby Website:

Try Using SEARCH
to Find What You Need. 
There are 1,000s of Pages Indexed on RF Cafe !

Electronics World Cover,TOC,and list of posted Popular Electronics articles QST Radio & TV News Radio-Craft Radio-Electronics Short Wave Craft Wireless World About RF Cafe RF Cafe Homepage RF Cafe in Morse Code Google Search of RF Cafe website Sitemap Electronics Equations Mathematics Equations Equations physics Manufacturers & distributors Engineer Jobs Twitter LinkedIn Crosswords Engineering Humor Kirt's Cogitations Engineering Event Calendar RF Engineering Quizzes AN/MPN-14 Radar 5CCG Notable Quotes App Notes Calculators Education Magazines Software,T-Shirts,Coffee Mugs Articles - submitted by RF Cafe visitors Simulators Technical Writings RF Cafe Archives Test Notes RF Cascade Workbook RF Stencils for Visio Shapes for Word Thank you for visiting RF Cafe!

Engineering & Science Technical Articles
(submitted by RF Cafe visitors)

RF / Microwave / Wireless Engineering & Science Technical Articles (submitted by RF Cafe visitors) - RF CafeNow you don't have to wait for a magazine to publish your technical article. If you would like to have your article posted here, please attach it to an e-mail in MS Word format (I will convert it to PDF) or PDF format, along with a brief description to use with the listing.

Suggested topics include radar, electronic warfare, commercial wireless, aerospace, semiconductors, system design, oscillators, amplifiers, filters, project management, component specification, testing, homeland security, defense technology and simulation.

Many thanks to all the contributors here for sharing your knowledge with our visitors. Articles listed here have been submitted by the original authors. Please direct any questions or comments to the authors.

Here are great articles printed in the trade magazines:

2006| 2007| 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014 | 2015| 2016 | 2017

Measuring Peak and Pulse Power
with USB Power Sensors

by Orwill Hawkins, LadyBug Technologies

As technology and measuring techniques advance, the time eventually comes when continuing to use old methods not only doesn't make sense, but can actually harm your reputation by providing data that cannot be duplicated by customers who long ago adopted the new ways. Orwill Hawkins, of LadyBug Technologies, has written a white paper describing how to make accurate, repeatable peak and pulse power measurements on waveforms using the precision of modern instruments that provide a graphical view of the entity being investigated. USB power meters provide an inexpensive means of obtaining high quality measurements and the benefits of a graphical display environment (on your computer) at a relatively low cost. I particularly like the use of the word 'mesial' in describing the midpoint of a pulse's rising and falling edges.

Aeromodeler Dave Wineland Awarded
the Nobel Prize in Physics

As you might know if you have been an RF Cafe visitor for a while, my life-long hobby has been model aviation. Many notable people have similarly been aeromodelers from a young age, including aircraft designer Burt Rutan, Space Shuttle astronaut Robert "Hoot" Gibson, radio personality Paul Harvey, actor and WWII bomber pilot Jimmy Stewart, Olympiad Bruce Jenner, catamaran and surfboard designer Hobart "Hobie" Alter, to name a few. Physicist Dr. David (Dave) Wineland has just been added to the list since he won the Nobel Prize in Physics in December 2012 for his work on quantum computing. The Academy of Model Aeronautics' (AMA) monthly magazine Model Aviation printed an interview with Dr. Wineland in the January 2013 edition, where he discusses his history with model airplanes and his work at the National Institute of Standards and Technology (NIST) in Boulder, Colorado. Model Model Aviation editor Jay Smith granted permission for me to reprint the article here on RF Cafe since it will likely be of interest to engineers and scientists who visit the website.

Reflect Forward Linearizer for Combined Amplifiers

by Ray Gutierrez, Micronda LLC

This paper is a continuation work for the “New High Efficiency Intermodulation Cancellation Technique for Single Stage Amplifiers.” Published in January 2008 on RF Café’s Paper section. The paper describes configurations for dual and multiple parallel amplifiers and uses the basic Reflect Forward technique for intermodulation cancellation. Some new improvements were made to the RFAL technique to improve the efficiency and operation.

LED Lighting vs. Incandescent Lights
for Commercial Buildings

Short write-up on benefits of LED lighting.

SPURS Software Article

by Kirt Blattenberger, RF Cafe

RF Design Magazine Software Contest Winner November 1992

I just ran across this magazine and decided to scan the article. It is a great tutorial on mixer spurious product calculation - if I do say so myself  ;-)

Who Invented Radar?

by Cornell Drentea

Here is a short treatise on the history of radar development, beginning in 1793 with Italian scientist Lazarro Spallanzani's experimentation on a bat's use of ultrasound for navigation, on up through modern systems.

Efficiency Measurements of Portable-Handset Antennas Using the Wheeler Cap

by Darioush Agahi and William Domino

In the design of wireless portable devices, antenna efficiency is a variable that can have a great effect on overall system performance, and yet may not always receive the attention it deserves. As an example, RF engineers must frequently make critical tradeoffs in receiver design in order to improve sensitivity by mere fractions of a dB, but a poor antenna efficiency can easily cause a degradation of several dB. This pitfall can occur in systems such as GSM, where many tests are performed using a cable connection to the antenna port; a handset may easily pass such tests, only to be later hampered by its antenna in the field. This paper is targeted at the very important parameter of antenna efficiency, and a measurement technique that can be used to quantify it.

Marconi's Legacy:
National Sovereignty Claims in Radio

by Robert Horvitz

Abstract: Presented at the 1st COMMUNIA Workshop on "Technology and the Public Domain," NEXA Center for Internet and Society, Politecnico di Torino, Italy, 18 January 2008.

Since early in the 20th century, national governments have asserted sovereignty over the electromagnetic spectrum. These assertions were initially embraced as a way to control the monopolistic ambitions and offensive business practices of the Marconi Wireless Telegraph Company. They are still the basis of radio regulation. However, as wireless communication moves to higher and higher frequencies - into the range of infrared (heat) and free space optics (light) - it is becoming obvious that claiming sovereignty over radio frequencies makes no more sense than claiming sovereignty over colors of the rainbow. Is radio legally different from light? If not, might we someday need government permission to use certain colors of light for certain purposes, as with the invisible colors of radio?

GSM Handset Power Amplifier Control Loop
Design An Analog Approach

by Jason Millard and Darioush Agahi

Power amplifier control (PAC) for a Global System for Mobile communications© (GSM©) compatible radio is one of the more challenging aspects of the GSM-based system design. Not only must the radio meet all output radio frequency (RF) spectrum specifications, but the Power Amplifier (PA) control loop must also be stable under varying environmental conditions. This paper starts by looking at the basic control theory, and discusses its advantages over simple open loop control. It then moves on to describe each block of the loop in detail. Stability is also discussed, and then finally, the paper examines a case study radio.

New High Efficiency Intermodulation
Cancellation Technique for
Single Stage Amplifiers

by Ray Gutierrez, Micronda LLC

New High Efficiency Intermodulation Cancellation Technique for Single Stage AmplifiersA new design configuration that uses the basic concept of the RFAL distortion cancellation technique. Previously published configurations using the RFAL uses two main amplifiers, the new configuration requires only one single main amplifier and low level MMIC amplifiers in the Intermodulation Cancellation Loop.

The basic RFAL technique uses the behavior of a transistor when driven into its non-linear operating region. At the high drive level the input reflects not only the fundamental components of the input signal but also the non-linear distortion components appearing at the output of the transistor. The level of the distortion products at the input is sufficiently proportional to the output such that it can be used and processed as a correction or error signal to cancel the output distortion of the transistor amplifier.

Block diagrams, schematics, data are included.

See follow-on work: Reflect Forward Linearizer for Combined Amplifiers

Spectral Leakage
in the Discrete Fourier Transform

by Greg Adams, with the permission of Lockheed Martin Company, NE&SS SS Math & Physics Seminar

Download Spectral Leakage in the Discrete Fourier TransformSynchronous sampling is typically used with a DFT when testing analog to digital converters in the laboratory. A pure sine wave test signal is generated at such a frequency that the input signal goes through a whole number of cycles during the sampling period.

If the test signal is slightly off frequency, i.e. the input signal doesn’t complete a whole number of cycles within the DFT time window, a distortion called spectral leakage occurs. A small frequency error has little effect on the main signal, but has a strong effect on the DFT noise floor.

The relationship between frequency error, and the signal to noise ratio due to leakage noise has been established. This relationship can be used to determine the frequency resolution which the sine wave generator must have in order to generate a sine wave at a sufficiently accurate frequency. A simple calculator program is provided to evaluate the equations.

ADC Toolkit: Used with presentation

The Study of Fast Adaptive Algorithms
and Introducing New Methods
for Increasing the Rate of Convergence
and Its Use in Smart Antennas

by S.Y. Skandari, Ch. Ghobadi, J. Nourinia, Urmia Univ.,  Urmia, Iran

Download The Study of Fast Adaptive Algorithms and Introducing New Methods for Increasing the Rate of Convergence and Its Use in Smart AntennasAlgorithms are introduced for increasing the rate of convergence in adaptive algorithms and new methods for selection of m step-size are given. Special functions are introduced for the definition of m which overturn current limitations and increase the rate of convergence and decrease noise.

Rigorous Analytical Expressions
for the Effective Dielectric Constants
of the Shielded Symmetrical Bandline

by Dr. Nasreddine Benahmed, University of Tlemcen, Algeria

A set of accurate closed-forms formulas for the effective dielectric constants of the shielded symmetrical bandline.

Software for Design NMR Probes Using
the Shielded Split Ring and the
Shielded Symmetrical Band Resonators

by Dr. Nasreddine Benahmed, University of Tlemcen, Algeria

Design NMR probes using closed-forms formulas of the primary and secondary parameters of the shielded split ring and the shielded symmetrical band resonators . These formulas are based on rigorous analysis by finite element method (FEM) , method of moment (MoM) and curves fitting techniques.

In-Building RF Coverage Solutions

by Shekar Kulashekaran,   shekar.pk@gmail.com

This presentation offers a methodical approach to planning and implementing in-building solutions for GSM 900 & 1800 MHz, and CDMA phone systems that helps solve the problem of coverage in offices, garages, shopping centers, etc. Shekar has 6 years of experience planning and installing these systems.

Power Amplifier Linearization
Using Diode On Voltage

by Mrunal A. K. & Makarand Shirasgaonkar - MTech Students, Dr. R. M. Patrikar, Professor, Visvesvaraya National Institute of Technology, Nagpur INDIA.

RF cafe - Power Amplifier Linearization White PaperThe emphasizes on higher data rates and spectral efficiency has driven the industry towards linear modulation techniques such as QPSK, 64 QAM, or multicarrier configurations. The result is a signal with a fluctuating envelope which generates intermodulation (IM) distortion from the power amplifiers. This paper describes a new approach of using a Diode as a predistorter in view of minimizing non linear distortion introduced by the high power amplifier in microwave radio links.

RF & Microwave
Power Amplifier Design

4-Part Lecture Presentation
(contains much material from book)

Click to view details on RF and Microwave Power Amplifier Designby Andrei Grebennikov, M/A-COM Eurotec

Note: If you get sign-in screens, just close the window and the file will load.

Lecture 1: Nonlinear Active Device Modeling
Lecture 2: Impedance Matching
Lecture 3: PA Design Fundamentals
Lecture 4: High Efficiency Power Amplifier Design

Design and Development of Low Noise Amplifier
Using 3-dB Quadrature Hybrids

by Vandana Kalibhat Ramchandra

This paper describes and discusses a procedure of how to design RF/Microwave Low noise amplifier with minimum noise figure and low VSWR. The initial data available is S-parameters of the device. This paper references the RF design tool called ADS by Agilent technology.

Short Wire Antennas: A Simplified Approach
Part I: Scaling Arguments

by Dr. Dan Dobkin veDr. Dan Dobkin version 1.0, enigmatics@batnet.com

In this article we shall try to illustrate a simpler and more direct way of understanding how short wire antennas, and by extension other small antennas, interact with traveling electromagnetic waves, in which we focus on the potentials that result directly from charges and currents.

Part II will follow if sufficient interest is shown in this first installment.

Tutorial of Satellite Communication

by Kamran Ahmed, Institute of Information Technology, University of Sindh, Pakistan

This is an excellent series of lectures on the basics of satellite communications.
           ▪ Overview of Satellite Systems
           ▪ Orbital Mechanics
           ▪ Orbital Perturbations
           ▪ Radio Wave Propagation
           ▪ Polarization
           ▪ Antennas
           ▪ Link Budget
           ▪ Interference
           ▪ Channel Characteristics

On the Physical Meaning of the Curl Operator

by Christopher K. Horne

RF Cafe - On the Physical of the CurlIn solving electromagnetic problems where the curl operator is evoked to compute the electric or magnetic fields, one often forgets the curl has a physical meaning. The purpose of this article is to support the mathematics of the curl with the physical meaning of its operation.

- See also: "Pulsed S-parameter Measurements for GSM Amplifiers", MP Digest, June 2004

Using Simulation Tools to Troubleshoot
an LC Filter Design

by Ed Troy, Aerospace Consulting, LLC

Almost everyone uses simulation tools for designing RF, microwave, and high speed digital circuits today. It is essential. But, very few engineers use those same tools for troubleshooting of circuits that are not working correctly. It amazes me that many engineers and technicians still spend days tuning, tweaking, and adjusting RF circuits that do not work properly on the bench. They could probably find, and fix, the problems in much less time by firing up their simulation software. It is much faster to change values, both known and speculated, in a simulation engine than it is to make the same changes on the test bench.

The Design of Ultra Narrow-band Amplifiers using Small Signal Varactor Up-converters for ESM, ECM, ECCM, and ELINT Applications

by Dr. Alfred I. Grayzel, Dr. Ashok (Ash) K. Gorwara, Paul Kuhn Planar Monolithics Industries, Inc.

A method is presented in this paper for realizing tunable amplifiers with bandwidths of less than 0.5%; without the use of superconductors and cryogenic cooling. This method uses a small signal varactor up-converter to achieve these ultra narrow bandwidths. The equivalent circuit for the up-converter is presented as well as the circuit configuration of the narrow band negative resistance amplifier. The design and experimental results are presented for a 0.5% bandwidth negative resistance amplifier at 800 MHz; using this unique circuit design. These devices and circuits can be used for electronic warfare applications such as surveillance, electronic reconnaissance, jamming and frequency hopping.

Reflection / Transmission Power Measurements

by LadyBug Technologies

Obtaining accurate, reliable, and useful measurements of RF power in the forward (transmission) and reverse (reflection) directions requires careful selection of test devices and detection equipment. LadyBug Technologies has produced a white paper describing a method for performing reflection and transmission measurements using a power sensor and a directional coupler. It includes a discussion on coupler directivity and impedance match as a factor in measurement accuracy.

Measuring Semiconductor Device Input
Parameters with Vector Analysis

by Joe Cahak, Sunshine Design Services

This article will cover a recent test experience that utilized some thinking about the test fixture, the bias requirements and the device mounting and special calibration offsets needed to de-embed the test fixture response from the device response within the test fixture. The device also had to have bias on several ports simultaneously. We had to establish a "reference plane" within the fixture, from which we can use the Vector Network Analyzer's Port Extension or Phase Offset to dial out the distance from our 1 port calibration reference plane to the point of short reference within the fixture. With this phase offset compensation we can then measure the device capacitance of the part within the fixture and the line length of the test fixture mostly worked out by the port extension.

RF Filter and RF SAW Filter
for Product Development

by John Lai, Oscilent Corporation

The purpose of this article is to discuss the important design considerations and development limitations of a Radio Frequency and Surface Acoustic Wave (SAW) Filter (Both IF Filter and RF Filter). Each of the major Electrical Parameters are discussed from a development perspective as follows (reference Figure 1 for further definition): We will also be reviewing RF Filter electrical components.

Understanding [Antenna] Polarization

by Brian B. Donalson

This is a technical paper written to support newly trained satellite operators. It helps in understanding how signals are received from orbiting satellites. Not too technical but if you are someone who wanted to learn a little about satellite communications, this is a good start.

Understanding Standard Off-Set vs. Inverted [Satellite] Dishes

by Brian B. Donalson

This is technical paper written to support newly trained Satellite Operators. It is a paper that shows the difference between a standard off-set satellite dish and an inverted off-set Satellite dish. Technical in nature, but easy to understand. Complete with illustrations to help you understand. A good read even if you know nothing about satellite dishes.

4G Technology - An Overview

A brief overview of the 4G system still in its planning and implementation (and definition) phase, provided by the folks at Broadband Expert.

A Graphical Approach to
Mixer Spurious Analysis

by Kirt Blattenberger, RF Cafe

The Spur Web chart rapidly identifies both inband and out-of-band spurs, affording a pictorial view of where conversion system frequencies lie with respect to all spur products.

RFDAC (RF Digital-to-Analog Converter)
White Paper

by Michael Hopkins, CurrentRF

RF Cafe - RFDAC (RF Digital-to-Analog Converter) White PaperA breakthrough in Digital to Analog Conversion and breaching the Nyquist barrier, any output frequency is now possible from low frequency digital data with the RFDAC. Achieve optimal baseband DAC noise and AC performance, clearing the way for true 12, 14, and 16 bit performance at any output frequency.

Polynomial Model of Blocker Effects on Small Signal Gain and Noise Figure for LNA/Mixer Devices Used in Wireless Receivers

by William Domino, Nooshin Vakilian, and Darioush Agahi

In designing today’s wireless handset receivers, it is important to maximize both receive sensitivity and resistance to undesired signals, also called “interferers”, or “blockers”. The starting place for receiver design is the calculation of budgets for noise figure and linearity, usually facilitated by a spreadsheet. While it is straightforward to find the cascaded noise figure (NF) and 1dB compression point (P1dB) using a spreadsheet calculation, it is often not clear how to use these to predict the actual performance of the receiver in the presence of a large blocker. To obtain a reasonably accurate prediction may instead require an inconvenient co-simulation of the system with circuit models embedded. However, a simpler approach is possible, which is still performed at the level of cascade calculations rather than simulation.

Expert Witnesses

The staff at IMS ExpertServices™ has prepared a few articles on the subject of expert witnesses.

Monolithic Ceramic Block
Combline Bandpass Filters

by Darioush Agahi, Sykworks

Small size and ruggedness are two important factors in the selection of bandpass filters for military and OEM applications. Monolithic ceramic block combline bandpass filters not only offer a size advantage in UHF through L-band frequencies; they also have other characteristics that make them extremely attractive when compared to other technologies. The filters are characteristically lower in cost and have relatively good insertion loss due to their high Q material (Q>10,000). This paper describes the design technique used for ceramic bandpass filters.

CAD Oriented Study of Polyimide Interface
Layer on Silicon Substrate for RF Applications

by Kamaljeet Singh and K Nagachenchaiah Semiconductor Laboratory (SCL), SAS Nagar, Near Chandigarh, India

Download CAD Oriented Study of Polyimide Interface Layer on Silicon Substrate for RF ApplicationsAbstract: Polyimide interface layer on standard silicon substrate extends the use of silicon for RF applications and is also compatible with the present CMOS technology. This paper investigates the characteristics of the microstrip lines patterned on polyimide interface layer up to 40 GHz. The limitation of lossy silicon substrate can be overcome by this approach. The full wave analysis of the microstrip line has been carried out using CAD tool. Also the non-ideal ground plane effects along with the concept of thicker bottom metallization below polyimide have been demonstrated to have lower losses.

Coupled Microstrip Filters:
Simple Methodologies
for Improved Characteristics

by Kamaljeet Singh, R. Ramasubramanian, S. Pal Communication Systems Group, ISRO Satellite Center, Bangalore, India

This paper presents improved characteristics of the hairpin filter topology. Standard hairpin configuration has the drawback of broader bandwidth, more insertion loss along with poor skirt rate. This paper demonstrates the approach to overcome the limitation inherent in hairpin as well as suppression of the harmonic which is prominent in the microstrip coupled filter topology.

Short Wire Antennas: A Simplified Approach

by Dr. Dan Dobkin version 1.0

Note: If you get sign-in screens, just close the window and the file will load.
Part I: Scaling Arguments
       How does a wire dipole antenna work?
       How do we find the resistance and the
       Why does the reactance vanish at an
        appropriate length or frequency?
Part II: Detailed Estimates of Scattered Voltage
            and Current
       We will now fill in the details of the calculation
       of scattered current and voltage for a short
       length of wire with an impinging potential
RF Cafe - Short Wire Antennas: A Simplified ApproachIn this article we shall try to illustrate a simpler and more direct way of understanding how short wire antennas, and by extension other small antennas, interact with traveling electromagnetic waves, in which we focus on the potentials that result directly from charges and currents.


"I will offer a $5 Starbucks gift certificate for each algebraic goof reported and corrected."

Smith Chart™ for Excel™

by Kirt Blattenberger, RF Cafe

This Excel workbook demonstrates how easy it is to implement a Smith Chart using only a standard x-y scatter chart and coordinate conversions.

Load Network Design Techniques for Class E
 RF and Microwave Amplifier

by Andrei Grebennikov, M/A-COM Eurotec
The output network of a class E amplifier must provide impedance matching at the fundamental frequency and adequate rejection of harmonic frequencies, while handling DC power to the device.

First-Time-Right Design of RF/Microwave
Class A
Power Amplifiers
Using Only S-Parameters

by Ivan Boshnakov (ivanb@aerial.co.uk), Senior Principal Engineer, Aerial Facilities Limited (www.aerialfacilities.com)

This article describes and discusses a procedure of how to design RF/Microwave Class A power amplifiers in a very efficient and highly accurate manner when the only initial data available are the S-parameters of the transistors. This paper references the "Tandem RF  Software Programs Streamline the Design of Power Amplifiers" item by Mr. Boshnakov toward the bottom of this page.

Maxwell's Primer (see series of links below)

by Glen Dash

This tutorial series is graciously provided by Dr. Dash: Part 1: An Introduction
Part 2: Why Things Radiate
Part 3: The Difference a Del Makes
Part 4: Equations Even a Computer Can Love
Part 5: Radiation From a Small Wire Element
Part 6: The Method of Moments

These articles provide a magnificently comprehendible presentation of Maxwell's Equations. They originally appeared in Conformity magazine in 1999, and were pulled a couple years ago. All six parts have been revised and condensed into a much small file size to facilitate easier downloads (as of November 15, 2005). Glen Dash is the author of numerous papers on the laws and standards applicable to electronic equipment. He is a graduate of MIT in Electrical Engineering and holds a law degree from Harvard. Please send a note of thanks to Dr. Dash for making these immensely popular articles available.

Automatic Telephone Call Indication Device
 Using Power Line

by Manu V Thayyil and Prince V Thachil, Model Engineering College, Thrikkakra, Kochi, India

This paper describes the design of an automatic telephone call indication device with power line as the channel for communication via Amplitude Shift Keying. These guys are graduate students and welcome feedback - manuthayyil@yahoo.co.in

Tandem RF Software Programs Streamline
 the Design of Power Amplifiers

by Ivan Boshnakov and Jon Divall, Aerial Facilities Ltd., U.K.

This article describes a procedure for the design and development of power amplifiers using harmonic-balanced software in tandem with impedance matching network synthesis software. For this purpose a particular design problem will be discussed.

The Noble Art of De-Coupling

by Carl Lodstrom
Tricks of the trade for successful use of capacitors for decoupling.

Criss-Cross RFAL Cancels
the IMD Distortion in Amplifiers

Download Criss-Cross RFAL Cancels the IMD Distortion in AmplifiersThis article provides a new design configuration that uses the basic concept of the RFAL (Reflect Forward Adaptive Linearizer) distortion cancellation technique.

The basic RFAL technique uses the behavior of a transistor when driven into its non-linear operating region. At the high drive level the input reflects not only the fundamental components of the input signal but also the non-linear distortion components appearing at the output of the transistor. The level of the distortion products at the input is sufficiently proportional to the output such that it can be used and processed as a correction or error signal to cancel the output distortion of the transistor amplifier. Author: Ray Gutierrez, Micronda LLC.