### An Amateur’s View on the P2: Diode Bridge and Gain Adjust [Part 3]

After a concise investigation on the P2’s oscillator and slew rate response, we proceed with the diode bridge and offset adjust blocks. A diode bridge can be configured as a double balanced modulator/mixer by adding transformers that “multiply” the signals, forming 2 sidebands. Remember that we can represent the trigonometric functions sin(x) or cos(x) with their complex exponential counterparts. When we do this for the product of 2 trigonometric functions and simplify, we end up with the sum of 2 trigonometric functions whose frequencies have been added and subtracted to each other. Therefore, we expect the output of the diode bridge to be a resultant wave composed of f1+f2 and f1-f2, given that f1 and f2 are the frequencies of the 2 input signals to the bridge.

Figure 1. Simplified block representation showing how the oscillator, diode bridge, P2 inputs and gain/phase adjust interact.

By doing this, DC-related noise is significantly reduced (since information from the input signal is now “encoded” in AC).

To get a better feel of the diode bridge, I have prepared a test setup below.

Figure 2. The internal schematic of the P2 diode bridge.
The inductors provide DC isolation, with a coupling coefficient of 1. Diodes D1, D2, D3, and D4 are identical, modelled with a zero-bias junction capacitance of 105pF [default=0] and saturation current of 3pF [default=0.01 pA]. The signal entering OPAMPIN+ to OPAMPIN- will be superimposed on the signal entering OSCIN1 to OSCIN2. The output is at DBROUT1, with its 180° phase shifted version at DBROUT2.

### Coupling 5MHz and 1 kHz sinusoids with the Diode Bridge.

Figure 3. Diode bridge test schematic for Case 1.

First, I test what will happen when I feed a 1 kHz and a 5 MHz sinusoid to the diode bridge block of the P2. Signal source/generator SS1 will supply the 1V pk-pk 1kHz sine wave while SS2 will provide a 5MHz signal of equal amplitude. I am theoretically expecting a signal with pronounced frequency components at 5MHz+1kHz and 5MHz-1kHz. Simulating yields the VOUT1 waveform below.

Figure 4. Simulation result of VOUT1 for test schematic in Figure 3.

Using the FFT to observe the frequency spectrum of VOUT1 yields the figure below.

Figure 5. FFT of VOUT1

Figure 6. Zoom-in view on the peaks of the FFT curve in Figure 5.

From the FFT plot, it is clear that the peaks are at 4.999 MHz and 5.001 MHz, verifying our theoretical expectations. Furthermore, the information in VSIG1 is visible at the envelope of VOUT1. Can you see it?

Figure 7. Where is the information of VSIG1?

Now we have an AC signal with information “riding” on it. All we have to do is amplify, then demodulate it before the output. Right? Not yet, there is one more bit of housekeeping that needs meticulous attention, and that is the diodes we choose for the bridge.

What happens when the diodes are mismatched? Let’s find out! Below, I’ve declared a new diode model, V48, with its saturation current at 7pA and zero-bias junction capacitance at 205pF.

Figure 8. Modified schematic for the P2 Diode Bridge. D2 has been mismatched.

Figure 9. Simulation result of Figure 8.

Mamamia! What has happened to our output? Can you imagine, increasing the saturation current by just 4pA and the capacitance by 100pF having such an effect on the output? To ensure that choice of values wasn’t a factor, I matched all the diodes again using V48, re-simulated, and got the proper waveform. It certainly must have been a daunting task to manufacture the P2 with 4 diodes that had such stringent matching conditions.

This isn’t the only instance matching played a crucial role in design. I believe the same rule applies for Kelvin bridges, or any similar circuit configurations, the only difference being a more relaxed demand in accuracy. How about current mirrors, who have to have MOS pairs that are identical to each other or else the “mirrored” currents would have offsets?

Figure 10. Schematic for adjusting offset in the P2.

This block isn’t the only one controlling the gain of the oscillator. Remember the C40 capacitor encircled in red back in part 1? I think it is meant to provide feedback from the AC demodulator (which makes sense, how can you demodulate/decode something if you have no idea or information on the code or original content used?) This discussion however, is for a future article.

Looking closer at the resistor-capacitor network, C11 and C12 are most probably variable capacitors, while R1 and R2 are potentiometers. Terminals GA1 and GA2 connect back to the oscillator while GADJIN1 and GADJIN2 connect to the outputs of the diode bridge. From part 2, we recall the most interesting component of the oscillator, C6, where the value of capacitance and amplitude of oscillation share an inversely proportional relationship, valid from 25pF to 1µF, after which oscillation stops. Looking back at Figure 10, I believe it is safe to assume that the capacitance will only vary in the pF range because series-parallel connections will cancel each other out. We should be surprised if we saw a capacitor here with a value of 1µF or more.

To conclude, let us simulate the schematic in Figure 1.

Figure 11. Simulation result of Figure 1.

Node 2 is the output of the diode bridge (shunted to the offset adjustment block). Node 7 is the input pulse to the diode bridge. Different combinations of x and y yield different results (less than 1 of course). When x and y are at very low values, the peak-to-peak voltage of node 2 approaches that of node 7. I think the default values set in Figure 10 are just right to prevent overmodulation.

Can you see the information riding on node 2?

### 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

### 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…