Common Emitter Frequency Response using EET

Even the simple common emitter circuit can result in some pretty complicated expression for the frequency response. The inclusion of a single element, the base-collector capacitance, introduces much complexity.  This circuit is analyzed in detail by most of the textbooks, including Gray & Meyer's.  None of them makes use the EET.  We give a derivation using Middlebrook's EET to see if the analysis is simplified.

 We work out the factor involving Cf,

This is a little bit less work than the more direct method,

The two methods produce the same expression, so using EET does not give more insight.  

The base-collector capacitor results in an additional pole and a right-hand side zero and shifts the dominant pole.  The dominant pole can be approximated from the input capacitance and the Miller capacitance.

Useful Circuits with Two Transistors

The preeminent circuit designer Barrie Gilbert asks "How many distinctly different and really useful circuits can be made with two transistors, anyway?"  and his answer "about twenty-four" (Williams, Analog Circuit Design, p179).  Let's see what they might be.  It is perhaps subjective to tell what is useful or different.  Also what type transistors, BJT, JFET, MOSFET?  Same circuit configuration with different type of transistors should not be considered distinct. What about other circuit elements?  Assume the passives, resistors, capacitors, inductors, are OK, but what about diodes? And what about a multi-emitter/collector transistor or a dual-gate MOSFET?  Is it considered one transistor or multiple transistors?

A single transistor has three basic amplifier configurations; it can also be configured as a diode, and the emitter-base junction also makes a somewhat usable Zener diode.  A JFET makes a good current source (current regulating diode).

Input Impedance of a Bipolar Transistor Bias with Feedback

AoE shows a bipolar transistor bias circuit using feedback from the collector.  AoE2 and AoE3 show the identical circuit, but they differ in the values of the input impedance: AoE2 states 300 Ohms and AoE3 200 Ohms.  We would like to analyze the circuit to see why the value has changed.  Here the base bias is established by a resistor from the collector, which has the effect of negative feedback: a high bias lowers the collector voltage that reduces the base voltage.  

Here we estimate the collector current to be about 1mA.  The input impedance is about 200 Ohms for a beta of 100; it does not exceed 225 Ohms as the beta goes to infinity.  So it seems justified that AoE3 makes the correction.   Even when the temperature varies, the input resistance stays relative constant.  For example, if T = 100C, VT = kT/q = 32mV, but because Vbe decreases with increasing temperature, the emitter current also goes up, Vbe = 0.4V, Ie = 1.34mA, gm is still around 1/25 A/V.

N Light Switches

AoE2 has an exercise asking readers to wire up N switches that any one of the switches can turn on or off a light bulb.   It comments that every electrician knows how to do this, but few electronic circuit designers do.  Given the hint that it requires 2 SPDT and N-2 DPDT switches, it is not hard to do.

This exercise is retained in AoE3.

A Current Source Circuit from AoE-X

H&H show a clever current source circuit and challenge readers to prove the circuit works especially without using two of the constraints.

It is a circuit of an opamp driving a bipolar transistor.  The base current of the bipolar transistor would normally cause an error.  Here the error is compensated.  The base current is sensed with the base resistor kR1; the emitter voltage is Vin with the differential voltage added using a circuit configuration resembling a difference amplifier.

Note that the current through R1 is the sum of the collector current, the base current and the current through R2, which the last two are the current through kR1.  The derivation makes no use of the constraints on the resistors.  The base current compensation is strictly accurate (assuming ideal opamp).

Home Lab On the Cheap

Computer: Raspberry Pi 4B ($50), Atomic Pi ($35), OrangePi Prime ($35)

Atomic Pi only has 2GB RAM, which limits its use; but it is PC compatible.  It is usable with a decent USB drive.  Raspberry Pi 4B is usable.  They all can run KiCad for PCB design.  Atomic Pi can run LTSpice.

Multimeters: ANENG AN8008 DMM ($20), ST213 Clamp meter ($20),  Cen-Tech/HaborFreight multimeter ($5), LCR-T4 ($6)
AN8008 gives pretty good voltage and resistor measurement but the current measurement is not reliable at high range. Cen-Tech's current measurement is good enough.  And ST213 is for high current.  LCR-T4 is also good for verifying component values and the firmware is open source.

Soldering Station: TS100 solder iron ($40 with coupon), Chandler Tools heat gun HG603D ($24), PCB Holder fixture ($4)
TS100 is pretty decent.  There is an open-source version of the firmware. It is portable with a battery pack.   I also got 3 more soldering iron tips for about $4 each: TS-KU, TS-JL02, TS-C1 in addition to TS-D24.  The 320W heat gun with two speeds works well.  The PCB holder works for small boards.  A Harbor Freight "Helping Hand" with two alligator chips and a magnifier is somewhat usable after I secured the base with a plate. 

Caliper: iGaging EZCal digital caliper ($29)
It has a nice large display and works except for the battery life.  It is relatively a little pricey.

Scale: Digital Jewelry Scale ($4)

200g range, 0.01g resolution.  It seems accurate.  Good for weighing small components.

Rotary Tools:  HarborFreight Chicago rotary tool set ($5)
This is a cheap tool, barely usable.  I power it with a variable voltage power adapter to make it somewhat usable.

Lights: Desk lamp with magnifier
It had a fluorescent lamp, but burnt out.  I installed 10 1W LEDs.  It works very well.

Hand Tools: Set of pliers, wire strippers, set of small screw drivers, nibbler, diagonal wire cutter, tweezers, 6" ruler in SAE and metric ($3 for 2), Dental picks and mirror ($6)
A Harbor Freight 16 in 1 electronic repair kit was inexpensive ($5) and usable.  A small diagonal wire cutter is very nice to have. 

ANENG ST213 Clamp Meter

For a total of $20.57, I received the ANENG ST213 Smart Digital Clamp Meter in 4 days (not bad for free delivery from China).  I have an ANENG AN8008 multimeter, which I have been generally pleased with.  I want to add a clamp meter to my measurement tools.

The meter looks slick and feels comfortable holding it.  It comes with one set probe and a K-type thermocouple.  The probe looks decent.  It takes two 2 AAA battery cells (not included).   If the battery voltage is less than 2.6V, the low-battery sign shows.  So NiMH batteries would have trouble staying above 1.3V per cell, but it probably still is functional at lower voltages.  Press the power button for two seconds to turn on.  The meter is in the auto mode, displaying temperature in Celsius and Fahrenheit (this is from the meter's internal temperature sensor since the thermocouple is not connected), which seems a little excessive to display the temperature so prominently when the thermocouple is not used.  There is an LED light at the top, which could be useful in the dark.

The "Smart" feature of the meter is that it tries to automatically determine what is being measured, AC/DC voltage, resistance with continuity beep, frequency and AC current.  But for resistance measurement, it is necessary to inject a signal, so the meter starts with voltage measurement and if the voltage is less than 0.5V, it switches to resistance measurement.  For low voltage measurement, it is necessary to manually select the mV measurement.  In many cases, it is probably not good to inject a signal and there is no way to manually select voltage measurement, which is the main deficiency of this meter.  And all measurements are autorange, no manual range selection.  This meter uses a single button for measurement selection and does away with the wheel, which can be a source of unreliability.

For voltage measurement, below 6V, the resolution is 1mV, which is good that the 5V circuit can be measured to 1mV unlike other meters that only go to 4V for the same resolution,  between 6V and 60V, the resolution is 10mV, and above 60V, 0.1V.  The voltage measurements generally agree with Fluke 87 DMM to 0.1-0.2%.  The accuracy holds up well above 100V.  

The resistance measurements agree with Fluke to 0.5%.  The meter beeps when the resistance is below 50Ω, which could be annoying.   Up to 0.5V could be applied.

For AC voltage, the RMS measurements seem good to 1KHz, with 3dB bandwidth around 3KHz.  The measurements agree with the Fluke to 0.6% below 1KHz.  The Fluke is still good at 10KHz with 3dB bandwidth over 100KHz.  Above 1V RMS, the frequency measurement works down to 6Hz; the resolution is 0.1Hz below 1KHz.

The main feature is the current measurement.  Below 0.3A, the current measurement is not useful; between 0.3 to 1A, the measurement error is around 10%.  Above 1A, the measurement error is about 2-3%, which is meeting the stated accuracy of +/-2.5% +/- 30 digits.  The initial offset can be nulled by pressing the REL|NCV button.  Note that it is possible to improve the low current measurements by looping the wire a few times around the clamp.  The jaw open to about 1".

For AC current measurement, the reading is 0 when the current is less than 0.6A and it is not expected to be accurate below 1A.  For a 100W light bulb, the Fluke reads 0.8A and this meter 0.63A.  When the Fluke reads 1.279A, this meter reads 1.15A, off by 10%.

It can also measure diode voltage and capacitance.  The max test voltage is 3.268V, and the max test current is about 2mA.  The test current is not constant, decreasing as the voltage increases.  The max diode voltages is about 3V, at which the applied current is about 0.16mA.  The capacitance measurements have a wider range than the Fluke, agreeing to about 5%.  

The NCV detection beeps when coming near a live AC wire (>90V).   It is sensitive enough to detect the live side of a wall socket.  On AC wiring, the live wire needs to be separated from the neural to be detected.  The Live wire detection uses only one probe; the actual detection threshold seems 1Vpp (tested with both probes connected).  These functions come handy in the household electrical work.

Dipping the thermocouple into molten solder, the temperature reading is 180C, which is about the melting point of 63/37 Sn/Pb solder.  At the other extreme, placing the thermocouple on dry ice, it drops to -40C and then shows OVLD (as specified).

This meter may be useful around the household and for automotive work, but not that good for lab electronics, especially because it cannot be locked in the voltage mode and making low current measurements.