Physics 4L (39L)

Overview of the Course

This laboratory course is the "beta" version of what will become Physics 4L, the laboratory course to accompany the Physics 4 series (4A-4E) for majors. The course consists of five projects in electrical circuits, four projects in optical circuits, and one project in data sampling and computational spectral analysis. A conceptual goal is to understand the same phenomena in real space and in Fourier space. This course was initiated by Prof. David Kleinfeld with the assistance of Mr. Sincheng Huang.

The course consists of a one hour lecture (Mondays at 12:00 PM to 12:50 PM in Mayer 2702) and a three hour laboratory (Tuesdays at 11:00 AM to 1:50 PM in Mayer 3574 (electrical) or 3722 (optical).

For Winter 2026, we were pleased to have Mr. Sincheng Huang and Mr. Phillip Neill as the class teaching assistants.

All Laboratory Reports and Homework should be sent as PDFs to Mr.Neill. They are due by Monday, 8:00 AM of the following week.

Diagnostic Exam
This diagnostic is used only to help set the pace of the course. Please do not use external resources. (0.1 Mb PDF)

Running schedule for Winter 2026

Week 1 (5 January): Kirchhoff’s laws, resistors, and ideal sources
Lecture notes 1 (2.2 Mb PDF)
Laboratory: Instruments and DC circuits (4.2 Mb PDF)
Regression handout (0.1 Mb PDF)
Homework 1 (0.3 Mb PDF)
Homework 1 solution (0.2 Mb PDF)

Week 2 (12 January): Kirchhoff’s laws using capacitors and inductors
Lecture notes 2 (1.5 Mb PDF)
Laboratory: Time dependent sources and measurements (2.0 Mb PDF)
RC time-domain analysis (0.2 Mb PDF)
Homework 2 (0.4 Mb PDF)

Week 3 (19 January): Convolution and linear response theory
This week has a holiday on Monday, so there is no lecture.
Laboratory: RC circuits in time domain (1.5 Mb PDF)
RC convolution with external drive (0.1 Mb PDF)

Ten stage RC ladder network with nodes 4, 7, 10 responding to voltage pulse


Week 4 (26 January): Temporal domain analysis of resonant circuits
Lecture notes 4 (0.1 Mb PDF)
Laboratory: RL circuits and RLC circuits in the time domainf (x.x Mb PDF)
RL time-domain analysis (0.2 Mb PDF)
Convolution integral in pictures (0.5 Mb PDF)
Review of damped oscillators (X.X Mb PDF)

Week 5 (2 February): Bode analysis of circuits
Lecture notes 5 (0.1 Mb PDF)
Laboratory: Amplitude and phase response (X.X Mb PDF)
Another view of convolution (X.X Mb PDF)

Series LC with only internal resistance of inductor


Week 6 (9 February): Frequency domain analysis of circuits
Lecture notes 6 (0.1 Mb PDF)
Laboratory: Bandwidth, period-doubling (x.x Mb PDF)

Week 7 (16 February): Aquisition and analysis of data
This week has a holiday on Monday, so there is no lecture.
Laboratory: Acquisition and numerical analysis data (xxx Mb PDF)
Spectral methods (5.3 Mb PDF)

Week 8 (23 February): The ABCDs of optics
Laboratory: Image formation (Chapter 6.1, Exercises 1-3) (15.2 Mb PDF)
ABCD matrices (2.3 Mb PDF)

Week 9 (2 March): Fourier optics 1
Laboratory: Fourier optics (Chapters 5.4 and 6.2, Exercises 4-6) (15.2 Mb PDF)

Week 10 (9 March): Fourier optics 2
Laboratory: Image formation in optics (Chapter 6.3, Exercises 7-23) (15.2 Mb PDF)

Data Sheets

Reading capaciter values (0.3 Mb PDF)
Reading resister values (0.1 Mb PDF)
Guide to decibels. Notes of Han Lin (0.1 Mb PDF)

Equipment Manuals

BK Precision 2831E bench voltmeter (1.2 Mb PDF)
GW Instek GPS 4303 quadruple power supply (2.7 Mb PDF)
Tektronix DPO2014B four channel 100 MHz oscilloscope (w/FFT) (6.9 Mb PDF)
Tektronix AFG2021 arbitrary function generator (3.4 Mb PDF)
Tektronix AFG1022 arbitrary function generator (5.3 Mb PDF)

Auxillary materials

Circuits; from Horowitz & Hill 2nd (3.7 Mb PDF)
Bode plots; notes of Harrison Wang (4.5 Mb PDF)
Fourier transforms; from Frederick & Carlson (0.5 Mb PDF)
Fourier series of full wave rectified sine wave; notes of DK (2.0 Mb PDF)
Complex integrals; from Matthews & Walker (0.1 Mb PDF)
Laplace transform for circuit analysis; notes of DK (0.7 Mb PDF)
Power; from Horowitz & Hill 2nd (0.1 Mb PDF)
Multi-stage filters; notes of DK (1.1 Mb PDF)