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### Fast Facts: Current Mirrors

The current mirror is very popular in IC design. But what does it do? As the name implies, it simply tries to provide a stable current source by "mirroring" the current of a reference branch. (Remember that current sources when loaded still provide the same amount of current, the voltage varying consequently). The current mirror is constructed by shorting a collector and 2 bases of 2 BJTs and a drain and 2 gates of 2 MOS.

Below is a futile attempt in simulation [back when I was still a college amateur].

In order to understand how the transistors provide equal constant currents, let us take the example below.

Above are 2 2N2222 NPN transistors functioning as a current mirror. Q2 has its collector shorted with the base. The 2 resistors are ohmic, so we can assume Ohm's law to be valid over that branch. The current supplied is 5 mA and 6.667 mA(initially) to Q2 and Q1 respectively. The bipolar junction transistor is a current controlled device. Thus, if the collector of Q2 is controlling the amount of output at the emitter of both transistors, and since both have approximately the same beta, hfe, or operating characteristics, the Ie flowing out of Q2's emitter approaches the Ie flowing out of Q1's emitter. Voltmeter XMM1 detects a current of 4.615 mA at Q2's emitter. (The ideal maximum forward beta of 2N2222 is 153.575)

10=(2k)It+0.7

It=4.65 mA initially

Q1 and Q2 start conducting. (Vce=0.2 V)

Now that It=4.65 mA(KCL), It=(beta)Ib+2*Ib (remember 2 bases), Ib=0.029889121 mA.

Ic=4.59 mA

Ie=Ic+Ib= 4.62 mA

Now for Q1:

Since Q1 and Q2 are shorted, both power supplies are electrically connected, thus:

10=(2k+1.5k)*(It/2)

It=5.714 mA=Ic

Ib=0.029889121

Ie=5.745 mA

(Both values are a little off tangent to the simulation, and the theory I applied above have assumptions. Anyhow, current mirrors provide two equal current sources in spite of the 500 ohm difference between the 2 resistors. If you have any comments, please feel free to leave them below.)

For educational purposes, here are cases where the resistors of the current mirror have varying resistances:

Unfortunately, the simulations above are quite spurious, since the circuit implementations are awry.

Simply put, current mirrors can mirror current because the terminals that control the current through the emitter-collector or source-drain terminals (i.e. the base and gate) are common to each other. (A simulation isn't really necessary)
Also, there may be minute differences in the mirrored current due to the 2 bases/gates drawing current from the collector/drain.

### Calculator Techniques for the Casio FX-991ES and FX-991EX Unraveled

In solving engineering problems, one may not have the luxury of time. Most situations demand immediate results. The price of falling behind schedule is costly and demeaning to one's reputation. Therefore, every bit of precaution must be taken to expedite calculations. The following introduces methods to tackle these problems speedily using a Casio calculator FX-991ES and FX-991EX.

►For algebraic problems where you need to find the exact value of a dependent or independent variable, just use the CALC or [ES] Mode 5 functions or [EX] MENU A functions.

►For definite differentiation and integration problems, simply use the d/dx and integral operators in the COMP mode.

►For models that follow the differential equation: dP/dx=kt and models that follow a geometric function(i.e. A*B^x).

[ES]
-Simply go to Mode 3 (STAT) (5)      e^x
-For geometric functions Mode 3 (STAT) 6 A*B^x
-(Why? Because the solution to the D.E. dP/dx=kt is an exponential function e^x.
When we know the boundary con…

### Common Difficulties and Mishaps in 6.004 Computation Structures (by MITx)

Updated:
May 6, 2018
VLSI Project: The Beta Layout [help needed]Current Tasks: ►Complete 32-bit ALU layout [unpipelined] in a 3-metal-layer C5 process. ►Extend Excel VBA macro to generate code for sequential instructions (machine language to actual electrical signals).
Current Obstacles/Unresolved Decisions:
►Use of complementary CMOS or pass transistor logic (do both? time expensive, will depend on sched.
►Adder selection: Brent-Kung; Kogge Stone; Ladner Fischer (brent takes up most space but seems to be fastest, consider fan-out) [do all? time expensive, will depend on sched.)
►layout requirements and DRC errors

Please leave a comment on the post below for advise. Any help is highly appreciated.

### Yay or Nay? A Closer Look at AnDapt’s PMIC On-Demand Technology

Innovations on making product features customizable are recently gaining popularity. Take Andapt for example, a fabless start-up that unveiled its Multi-Rail Power Platform technology for On-Demand PMIC applications a few months back. (read all about it here: Will PMIC On-Demand Replace Catalog Power Devices?) Their online platform, WebAmp, enables the consumer to configure the PMIC based on desired specifications. Fortunately, I got a hands-on experience during the trial period (without the physical board (AmP8DB1) or adaptor (AmpLink)). In my opinion, their GUI is friendly but it lacks a verification method for tuning (i.e. the entered combination of specs). How would we know if it will perform as expected or if there are contradicting indications that yield queer behavior? Also, there is not just one IP available, but many that cater to a differing number of channels and voltage requirements (each with their own price tag).
Every new emerging technology has the potential to oversh…