Staircase Generator

Staircase generator circuits have important applications in video systems. There are several ways to generate staircase waveforms, using 

The schematic of the staircase generator circuit is shown in Fig. 7.18. Not shown in the schematic is the power to the JK flip-flops and the AND gate. A +5-V DC input was used to power the digital ICs. 

The staircase generator circuit was constructed in all three simulators and in the lab by using real components. The breadboard used a 

UA723 for the op-amp, CD4027 for the JK flip-flops, and a CD4081 for the AND gate. 

Note that the PSpice results are shown in a slightly different configuration because of the PROBE waveform display program. Three of the four Q output waveforms are shown in the lower section of the plot (analog waveform), while the clock (a digital signal) is shown at the top. 

---

Figure 31 The devil s staircase generated by solving the sine circle map for a range of values of (I with K = 1.0. (From Ref. 75 used with permission.)...

A fast rise time potentiostat system based on the circuit described is shown in Figure 2-33. This system features a programmable waveform generator board for general simulation of waveforms and a waveform analyzer to digitize and store the data. The present setup features cyclic staircase generation (2.5mV/step) and double potential step experiments. 

This is used in the sigma-delta modulator (Fig. 10). In this case, the staircase generator is not needed, since the feedback integration and the input signal integration are performed by the unique integrator after the sum point, and simple 1-bit A/D and D/A do the job. 

At Tonic, the generation named Britney walked up and down the steel staircases, balancing their martini glasses with perfect form, gripping them gingerly at the rim. 

A hold device is always needed in a sampled-data process control system. The hold converts the sequence of impulses of an impulse-sampled function/(, into a continuous (usually staircase) function/g,). There are several types of mathematical holds, but the only one that is of any practical interest is called a zero-order hold. This type of hold generates the stair-step function described above. 

With the advent of digital implementation of electroanalytical experiments came the technique called staircase cyclic voltammetry, wherein the triangular wave is approximated by a series of small potential steps. The reason for such an approximation is partly due to the impossibility of digitally generating a pure ramp and more importantly to the realization that substantial improvements accrue from sampling the current at the end of each step, where double-layer charging has decayed away. If the steps are small, the data will fit theory based on pure ramps quite well. 

Figure 23-21 Generation of a square-wave voltammetry excitation signal. The staircase signal in (a) is added to the pulse train in (b) to give the square-wave excitation signal in (c). The current response At is equal to the cuirent at potential I minus that at potential 2.

In fact, many instruments now generate linear scan waveforms as staircase functions with very small (< 0.2 mV) A , because it is simpler to do so with digital control systems. When ISE is reduced below the level of the noise on the waveform, the distinction between staircase and linear functions is lost. 

Because each base pair contains a purine bonded to a pyrimidine, the strands are equidistant from each other throughout. If two strands that are equidistant from each other are twisted at the top and the bottom, they form a double helix (Fig. 12.9). In the double helix of DNA, the base pairs that join the two strands are stacked like a spiral staircase along the central axis of the molecule. The electrons of the adjacent base pairs interact, generating stacking forces that, in addition to the hydrogen bonding of the base pairs, help to stabilize the helix. 

Escape routes, staircases, and railings shall also be provided at appropriate places. Alternate lights in plant shall be given supply from alternate power feeders. This wiU prevent total darkness in the plant in case of power failure of one feeder. There shall be easy approach to diesel/gas generator sets for the supply of power in case of need (for emergency power supply) when grid power fails. However, these sets shall start automatically whenever grid power supply fails. 

U(x) is twice the generating function of staircase polygons. The loop class exponent is c = 3/2. The generating functions V and U have critical points xy — 1/2, xy = 1/4 and Wc = 1, i.e., a phase transition occurs at T = oo. (If the empty path would not be allowed, a phase transition would occur at a finite temperature). The free energy f w) is... 

---