Method reduces quantization errors using new digital circuit. Circuit provides very high resolution (10 to the minus 2nd power to 10 to the minus 3rd power Hz) without high-speed counters. It lends itself to microminaturization and is simple to construct. Unknown frequency is compared to standard frequency by means of zero-crossing coincidence-detecting circuit

Nossen, E. J.

Starner, E. R.

English

NASA Technical Reports Server

November 1974	 B74-10191 
NASA TECH BRIEF 
Lyndon B. Johnson Space Center 
NASA Tech Briefs announce new technology derived from the U.S. space program. They are issued to encourage 
commercial application. Tech Briefs are available on a subscription basis from the National Technical Information 
Service, Springfield, Virginia 22151. Requests for individual copies or questions relating to the Tech Brief program may 
be directed to the Technology Utilization Office, NASA, Code KT, Washington, D.C. 20546. 
Reduction of Quantization Error in Measurement of Frequency 
.
The problem: 
In modern electronic systems, such as radars, colli-
sion avoidance, altimeters, and navigation systems, 
frequencies are measured by counting the integral 
number of periods per time interval. However, there 
is always a quantization error involved in counting 
because a fraction of a period must be missed. Several 
techniques have been tried to reduce this error, for 
example: 
(a) averaging of the quantization error over a longer 
time interval, 
(b) use of high-frequency oscillators to increase reso-
lution, and 
(c) multiplication of the frequency by some constant. 
However, these techniques may extend processing time, 
High-Frequency ComponenS 
4	
Pulse 
Generator
not provide sufficient error reduction, and may require 
high-speed counters.. Sometimes these techniques may 
become another source of error. 
The solution: 
A more precise method reduces quantization errors, 
using a new digital circuit. The circuit provides a very 
high resolution (lO_2 to iO Hz) without high-speed 
counters. It lends itself to microminiaturization and is 
simple to construct. 
How it's done: 
Basically, the unknown frequency is compared to a 
standard frequency by means of a zero-crossing co-
incidence-detecting circuit. The process is an electronic 
Counter 
Buffers __________I Computer 
or Display 
Pulse fo j44 Counter 
.
	
Figure 1. Coincidence Detector and Frequency-Counting Circuit
(continued overleaf) 
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Government assumes any liability resulting from the use of the 
Aeronautics and Space Administration. Neither the United States
	
information contained in this document, or warrants that such use 
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will be free from privately owned rights.
https://ntrs.nasa.gov/search.jsp?R=19740000191 2020-03-17T13:52:34+00:00Z
I! 
—r
Count of Both 
Frequencies 
for Time T 
Zero-Crossing 
Pulses (0 
AND 
Gate 
Signals	 --
LI.	 N
Zero-Crossing 
Pulses (f0) 
Time
	
. 
Counter 
Triggers
No 
H	 n	 ih 
T _______I Stop 
I	 Start	 k- D2 
Command	 Command 
Start	 Stop
Coincidence 
Pulses 
Figure 2. Timing Scheme 
equivalent to that of the mechanical vernier caliper. In 
the vernier caliper, the measurement precision is ex-
panded by reading the coincidence of the scale markings 
of two nearly equal scales. The digital method uses an 
analogous approach. It employs zero crossing of a 
known stable frequency and the unknown frequency as 
the "scale markings," and a coincidence-detector circuit 
to determine where a zero-crossing coincidence has 
occurred between the two frequencies. 
In the circuit shown in Figure 1 an unknown 
frequency f and reference frequency f0 each feed into 
two paths, counters and pulse generators. The counters 
are actuated for the time interval determined by the 
coincidence detector, and the pulse generators convert 
the signals to a train of narrow pulses (1 to 100 
nanoseconds is typical) every period at the zero crossing 
(see Figure 2). The pulses are fed to an AND gate which 
generates a pulse whenever the two input pulses co-
incide. As an optional feature buffers are employed to 
store the counts for periodic sampling by a computer 
or to drive a display. 
The output pulse from the AND gate is used as a 
trigger to start and stop the counters. The time between 
the start and stop is the time interval over which the 
frequency is measured. This interval is obtained from 
the count in the reference-frequency counter, i.e., 
r= N0/f0 
where N0 is the count of reference frequency f0 . The 
unknown frequency f is derived from its measured
frequency counter N and the previously measured line 
interval r as follows: 
N N 
f= — = — f T N0 
Note: 
Requests for further information may be directed to: 
Technology Utilization Officer 
Johnson Space Center 
Code AT3 
Houston, Texas 77058 
Reference: TSP74-10191 
Patent status: 
This invention is owned by NASA and a patent 
application has been filed. Inquiries concerning non-
exclusive or exclusive license for its commercial develop-
ment should be addressed to: 
Patent Counsel 
Johnson Space Center 
Code AM 
Houston, Texas 77058 
Source: E. J. Nossen and E. R. Starner of 
RCA Corp.
under contract to

Johnson Space Center 
(MSC-14649) 
B74-10191	 Category 02


Reduction of quantization error in measurement of frequency

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