Camenzind_Analog design chips

Judging by the frequency response alone, the Chebyshev filter has the sharpest response, though it produces some ripples in the pass-band (i.e. below 10kHz). This ripple can be reduced, at the expense of steepness above 10kHz. In even-order Chebyshev filters the ripples are above the line (0dB in this case); in oddorder ones they are below the line.

The Bessel filter gives a gentle roll-off with no overshoot in the pass-band, and the performance of the Butterworth filter is in between the other two.

see elaborate tables giving you coefficients for Butterworth, Bessel and Chebyshev functions. This is no longer necessary. There are a multitude of programs available on the web (many of them at no cost), which calculate these values for you. Search for "active filter software".

Bessel, Chebyshev and Butterworth

Friedrich Wilhelm Bessel (1784 to 1846) was a professor of astronomy at the University of Königsberg in Germany. By measuring the position of some 50,000 stars he greatly advanced the state of celestial mechanics and came up with the Bessel function, which was found to be also useful in filters.

Pafnuty Chebyshev (1821 to 1894) taught mathematics at the University of St. Petersburg. His major contribution was the theory of prime numbers but, similar to Bessel he left behind a function which later turned out to be applicable to filters.

Of Stephen Butterworth we know only that he worked at the British Admiralty for almost all his life. In 1930 he published a paper "On the Theory of Filters". He died in 1958.

frequency and phase response, but they differ in sensitivity, i.e. how much component and op-amp parameter variations will influence filter performance. A temperature and Monte Carlo analysis reveals the merits.

High-Pass Filters

Band-Pass Filters

Although the arrangement is called a second-order band-pass filter, the drop-off rate is only first-order, 20dB per decade, since only one pole is active in each frequency segment. We can of course improve this by adding more stages, each stage contributing another 20dB per decade drop-off. And here there is a bewildering number of schemes available, with names such as Wien-Robinson, Deliyannis, Fliege, Twin-T, MikhaelBhattacharyya, Berka-Herpy and Akerberg-Mossberg. Your filter program will tell you which one to choose.

There is also an additional choice for the frequency response: compared to the Chebyshev filter the elliptic (or Cauer) has an even steeper initial drop-off, but the attenuation in the stop-band (i.e. outside the passband) is not flat.

Fig. 13-18: A fourth-order, twin-T elliptic band-pass filter.

components, but the values of most

capacitors and some of the resistors are such that they cannot be integrated. A fourth-order low-pass or high-pass filter requires at least eight external

components and five pins. For a band-pass filter with only modest performance 14 external components and pins are needed.

Switched Capacitor Filters

voltage or the current flowing into the capacitor for a certain period of time. In the case of figure 13-20, the current flowing between the two terminals over one period is

If we had a resistor between V1 and V2 instead of the switches and the capacitor, the current flowing through it would be:

I = (V1 − V 2)

R

Thus the equivalent resistance of the switched capacitor is:

1

R =

CR fclock

Let's look at some numbers. Suppose the switching frequency is 100kHz and CR = 5pF:

Thus, with a relatively small capacitor we can create the equivalent of a large-value resistor. If we were to implement such a device directly, the cost in area would be prohibitive.

But the area reduction is just the first benefit of switching; there is more: if we use this resistor in a filter, the absolute capacitance value disappears.

If we make the two capacitors equal (any value) and switch at a rate of 100kHz we get a filter with a cutoff frequency of 15.9kHz. If CR is ten times the size of C and the clock

frequency remains at 100kHz, the cutoff frequency decreases to 1.59kHz. Thus, the switched-capacitor filter has two significant advantages

over the active (linear) one:

1.A low cutoff frequency can be achieved with capacitor values small enough to allow integration.

2.The cutoff frequency is not influenced by absolute variations. Given an accurate clock frequency and capacitor ratios of 1%, the cutoff frequency will be within 1%.

The simple low-pass filter can be expanded into any of the configuration discussed under active filters. Take for example the Sallen & Key filters in figure 13-7. In a switched-capacitor design you would first

greatly reduce the values of the capacitors and then replace the resistors with a capacitor and switches.

The switched-capacitor filter requires lateral switches, which are easily implemented in CMOS, but cumbersome (and slow) in a bipolar process. For this reason, this approach has become exclusively CMOS

There are three disadvantages with switched-capacitor filters:

1.No matter how carefully you design the switches, there is always some switching noise.

2.A switched-capacitor filter samples the signal. To get an adequate sample, the highest signal frequency cannot exceed about 10% of the clock frequency. If there are signals present above that point, the switchedcapacitor filter will produce a mixture of new frequencies, some of which may appear in the 0 to 10% frequency range. To avoid such false signals, a linear (active) filter must be used at the input (an anti-aliasing filter).

3.A switched-capacitor filter can only be simulated in real time, i.e. with a transient analysis; you cannot take advantage of the many features of an AC analysis, such as measuring frequency and phase response. And with the clock frequency necessarily being high, simulation takes far more time compared to an active filter.

4.The output has sampled noise, which is present even if the input is zero.

14 Power

Linear Regulators

Let's say you have 12 Volts available but need 3.3. Your 3.3-Volt load consumes up to 500mA. The 12-Volt source (e.g. a car battery) fluctuates between 10 and 14 Volts; the lower voltage needs to be within 5%.

The immediate choice to effect this change in voltage is a linear regulator. Look at it as a variable resistor, dropping whatever voltage is not needed.