ENGR 1 Presentation Thomas Matthews

My Background Sacramento State UC Davis San Jose State 1995-1998 Sacramento State 1999-present EEE Chair, 2013-2018 Advising Fellow 2018-2019

Motivation Say something about how engineers address problems – a “scaffold” for separating parts that can be separated and showing how the parts are connected Talk about analog and digital circuits Include some interesting examples

An Example Question There is a device that can have only one button to push. The one button causes three different actions. Whenever you push the button, the device does the action that you want. What is that device?

State Machine Example Answer – A Garage Door Opener The button is an input. There are other inputs. The output of the system is the motor drive (up, down, or stop). The output (i.e., the motor drive) depends on the input and on the state of the system.

Garage Door Opener What states are needed? Door down; Motor off Door up; Motor off Need States for motor driven

These states cannot continue indefinitely! More inputs are needed. States for Drive Motor These states cannot continue indefinitely! More inputs are needed.

Limit Switches When door arrives at down position, the lower limit switch (LLS) activates When door arrives at up position, the upper limit switch (ULS) activates

Summary Four states with outputs: Three inputs: 1 – door down, motor off 2 – door up, motor off 3 – moving down, motor ↓ 4 – moving up, motor ↑ Three inputs: button Upper limit Lower limit If door is in State 3, lower limit switch (LLS) causes State 1 If door is in State 4, upper limit switch (ULS) causes State 2 If door is in State 1, a click* causes State 4 If door is in State 2, a click* causes State 3 *A click corresponds to pushing the button

Input-Output Relationships State Diagram Output Table State 2 3 1 4 Motor Off— On ↓ On ↑ Arrows are labeled with the input that causes that path

Button input while moving Add Click in State 3 goes to State 4 New state State 5 – “Stop” Click in State 4 goes to State 5 Click in State 5 goes to State 3 Click inputs while door is moving

Another Look State 5 has the same motor drive as State 2; same output. A Click in State 5 and a Click in State 2 both go to State 3; same next state. Do we need State 5?

Equate State 5 with State 2 If the output is purely the motor drive, State 5 is the same as State 2. The only difference is that a click causes the transition to State 2 instead of ULS.

But wait . . . The position of the door in State 5 is not necessarily the same as in State 2. If the position of the door is the output, then State 5 is different from State 2 because they do not have the same output.

System States How are states represented? A voltage or a current (an analog value) A binary number. e.g., 11010110 One voltage for a “1,” e.g. +5V A different voltage for a “0,” e.g. 0V

Example: Analog Time Delay A resistor-capacitor circuit is built Switch closes at t =0 Capacitor voltage vC starts to increase vC crosses threshold voltage vTH after delay Detect this condition to get output

What Can Cause Error? Delay time depends on resistor and capacitor values – these are not exact and can change over time and with temperature Noise can cause a false output Delay time depends on Supply (VX) and on threshold (VTH). Adjusting VTH for a long threshold causes sensitivity to noise

Illustration of Sensitivity Slow changes in capacitor voltage mean that it is near the threshold voltage for a large range of time values Small noise or error in voltage causes large error in delay time

Example: Digital Delay A counter changes state (goes one higher) every time it is clocked after there is an input. Yes, it can have 1000 or more states Here, the counter counts to 1000, going up by 1 every millisecond. Result: one-second delay. What limits accuracy?

Digital vs. Analog Systems made with simple passive components (e.g., resistors and capacitors) have states, but they are continuously changing and their changes are governed by circuit components and by physical laws. Digital systems are more complicated to build, but states change only at known times and how states change is up to the designer.

Analog Signal Processing This input signal could be analog audio (e.g., your headphone output). This circuit would reduce high frequencies (a treble cut filter). The output can be calculated as a weighted sum of the previous output (i.e., state) plus the change due to the input over infinitely small time steps.

Digital Signal Processing (DSP) All signal sources are continuous variables and are first acquired as analog values We have to convert samples of these analog values into digital form (e.g., 8-bit words) using an analog-to-digital converter (ADC)* The number of samples per second is the sample rate. ADCs are an example of mixed-signal integrated circuit (IC) design *Note the method of defining an acronym and that compound adjectives are hyphenated

DSP In the digital domain, the output can be calculated as a weighted sum of previous outputs and inputs plus the change due to the input. The time steps are of a given size. This method can be used to make processors that adjust frequency response, cancel echoes, cancel continuous noise, make noise less perceptible, etc.

Analog vs. Digital Digital systems have some immunity to noise, at the expense of complexity The subsequent state of the system can be whatever you want within the limits of your processing power. All circuitry is inherently analog. Analog circuits are used to implement digital systems.

Interesting Fact The IEEE standard for gigabit ethernet over CAT5 cable has 21 different analog levels. The first operations done by the receiver use analog processing and are followed by an analog-to-digital converter. For each of the four wire pairs, the signal is sampled at 125 MHz producing 8-bit digital words, each word representing 2 bits of actual transmitted data. 250Mb/sec x 4 = 1000Mb/sec