Nuts & Volts - January 2005

In The Trenches

account for the worst case scenario. Otherwise, failures will occur. Some failures are trivial. Others can be catastrophic. No good engineer tolerates a failure based on faulty error estimates or wishful thinking.

So, why is the above frequency error not the absolutely worst error possible? It's because the accepted practice is to measure the frequency of a signal with the zero crossing points. There are two basic reasons for this. The first is that it's pretty easy to determine the zero crossing points. The second is that the steep-est slope of the sine wave is there, which makes the measurement the most precise. The error calculated above is the worst case using standard engineering practice.

The phase error is not measured that way because proper phasing implies that there are two systems working together. (Any phase measurement must relate to another phase measurement.)

Typically, phase measurements are used in motors or positioning systems. In such applications, phase comparisons are required over the whole 360 degree range. Therefore, the worst case error must be defined for a full 360 degrees. This is very different from the frequency measurement that only required two points on that 360 degree interval.

expect a decrease in error that is equal to the square root of the number of measures. (Four measures reduces the error by a factor of two; 100 measures reduces it by a factor of 10.) There are other, more complicated methods, as well. No error reduction system is suitable for every application. Be sure the method you choose is appropriate.

Conclusion

Using a basic low speed A/D is not always as simple as it first appears. Amplitude, frequency, and phase errors may be much larger than expected. Knowing how to anticipate and calculate these errors is an important part of data acquisition. NV

Reducing the Errors

ATMEL AVR ® Based Controller

Micro64

AVR ® Based Controller

Pin 1

www.micromint.com

Optional 2-channel 12-bit ADC 8-channel 10-bit ADC 8 Single-ended Channels 7 Differential Channels 2 Differential Channels with Programmable Gain (1x, 10x, 200x) Byte-oriented Two-wire Serial Interface (I2C) Dual Programmable Serial USARTs 1 TTL 1 RS-232A, RS-422, or RS485 Master/Slave SPI Serial Interface

Two 8-bit Timer/Counters with Separate Prescalers and Compare Modes Two Expanded 16-bit Timer/Counter with Separate Prescaler, Compare Mode, and Capture Mode Two 8-bit PWM Channels 6 PWM Channels with Programmable Resolution from 1 to 16 Bits Programmable Watchdog Timer with On-chip Oscillator 29 Digital I/O that can sink or source 20 mA

Small size - 1.5" x 2.1" x 0.52

Dual powered - operates on +5V or 6.5-20V at 55 mA (typical)

Program and Data Memories

64k or 128k Bytes of In-System Reprogrammable Flash with 10,000 Write/Erase Cycles

2 or 4 K Bytes EEPROM with 100,000 Write/Erase Cycles

36K Bytes SRAM Programming lock for Software Security

Peripheral Features

Starting at $119 ^{- Single Qty}

6P WM Programmable Lock

2 USART

Channels for Software Security

64 or 128k _Flash_ATmega64_{I2C Bus}OR

4k Bytes

SRAM ATmega128 ^{SPI Bus}

2k or 4k Programmable 8-Chan. EEPROM Watchdog Timer 10-bit ADC

Line Receiver Line Driver 29

12-Bit ADC Optional

Micro64 or Micro128 Connector

Serial I/O RS-232A, RS422 RS485

Digital I/O

2

+V(8-16VDC Unregulated)

VBAT

12-Bit ADC Optional

5V Regulator

32k SRAM

Real-Time Clock Calender Optional

There are two common ways to reduce basic errors at the A/D. As noted above, you can increase the sampling speed or increase the resolution. You can also use software. Probably the easiest method is to use multiple measures. I've discussed this previously in my "Statistics" columns (May and June 2004). Very briefly, you can increase the precision of a system by taking repeated measurements of the same signal and averaging them. The noise in the measurements will tend to cancel, while the true signal will tend to reinforce itself.