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Build Your Own Clock With Analog Dials, Part 1

Build Your Own Clock With Analog Dials, Part 1

This project turns old-school analog ammeters into a working clock that can also display the ambient temperature.


Introduction to the Gilbert Multiplier

Introduction to the Gilbert Multiplier

This article explores the Gilbert cell, a widely used analog multiplier circuit.


Second-Order Type-2 PLLs: Bode Diagrams, Bandwidth, and Overshoot

Second-Order Type-2 PLLs: Bode Diagrams, Bandwidth, and Overshoot

Learn how to select the zero frequency, damping factor, and loop bandwidth for one of the most popular PLL configurations.


Introduction to Second-Order Type-2 PLLs

Introduction to Second-Order Type-2 PLLs

This article explains how Type-2 PLLs with an integrator loop filter outperform Type-1 systems. To do so, we'll examine the PLL behavior for frequency step and frequency ramp inputs.


Understanding the Time-Domain Response of PLLs With Lag-Lead Filters

Understanding the Time-Domain Response of PLLs With Lag-Lead Filters

In this article, we examine how adding a zero to the PLL loop filter affects the transient behavior and steady-state errors.


Exploring the Bode Plots of PLLs With a Lag-Lead Loop Filter

Exploring the Bode Plots of PLLs With a Lag-Lead Loop Filter

In this article, we derive design equations for a second-order PLL with a lag-lead filter by examining its Bode plots.


Introducing the Lag-Lead Filter

Introducing the Lag-Lead Filter

Learn how using a pole-zero loop filter improves PLL performance and design flexibility over the simpler lag filter.


Analyzing the Lag Filter’s Effect on PLL Performance

Analyzing the Lag Filter’s Effect on PLL Performance

In this article, we evaluate the designs of two simple frequency synthesizers to learn how a second-order PLL with a lag filter can provide a faster rise time than a first-order PLL.


Understanding the Limitations of the Second-Order Type-1 PLL With a Lag Filter

Understanding the Limitations of the Second-Order Type-1 PLL With a Lag Filter

In this article, we analyze the steady-state errors and Bode plots for a second-order PLL with a simple, first-order loop filter.


Introduction to Second-Order Type-1 PLLs

Introduction to Second-Order Type-1 PLLs

Learn how adding a lowpass loop filter to a PLL with a single integrator impacts both the frequency-domain and time-domain response.


Understanding the Limitations of the First-Order PLL

Understanding the Limitations of the First-Order PLL

Higher-order PLLs are more commonly used than first-order PLLs. To explain why, we explore the first-order PLL's behavior in response to two inputs: a frequency step and frequency ramp.


Analyzing First-Order PLLs Using Linear Models

Analyzing First-Order PLLs Using Linear Models

In this article, we'll use the linearized model of a first-order PLL to understand its response to a simple input change. We'll then use Matlab simulations to visualize the signals.


Building a Push-Pull Level Shifter to Connect an MCU and a Low-Voltage Display

Building a Push-Pull Level Shifter to Connect an MCU and a Low-Voltage Display

In this project, we'll build and demonstrate a discrete analog solution to the incompatible logic levels of an Arduino Uno and an Elecrow e-paper HMI display.


Projects Nov 23, 2025 by Don Wilcher
Analyzing a First-Order PLL in Acquisition Mode With a Nonlinear Model

Analyzing a First-Order PLL in Acquisition Mode With a Nonlinear Model

In this article, we'll use a nonlinear mathematical model to improve our understanding of how a first-order PLL locks to a signal.


Foundations for PLL Nonlinear Analysis: Modeling the Phase Detector and VCO

Foundations for PLL Nonlinear Analysis: Modeling the Phase Detector and VCO

The phase-locked loop (PLL) is widely used in contemporary analog and digital communication systems. In this article, we develop a nonlinear model for the analog PLL by analyzing its key components.


Basic Principles and Implementation of the Quadrature FM Demodulator

Basic Principles and Implementation of the Quadrature FM Demodulator

Learn how an analog multiplier or AND gate can function as a quadrature detector for FM demodulation.


FM-to-AM Conversion Using the Foster-Seeley Discriminator

FM-to-AM Conversion Using the Foster-Seeley Discriminator

Learn how the Foster-Seeley discriminator, a classic analog circuit for FM demodulation, achieves its superior linearity.


Understanding Slope Detectors for FM Demodulation

Understanding Slope Detectors for FM Demodulation

In this article, we'll analyze the single-tuned discriminator for FM-to-AM conversion. We'll then discuss the balanced discriminator and how it provides improved linearity across a wider bandwidth.


Introduction to Frequency Discriminators for FM Demodulation

Introduction to Frequency Discriminators for FM Demodulation

In this article, we will examine the basic principles of FM demodulation through the simplest frequency discriminator: a differentiator.


FM Generation Techniques: Solved Examples

FM Generation Techniques: Solved Examples

In this article, we'll solidify our understanding of the reactance modulator and Armstrong modulator circuits by working through a series of design problems.