427
COMMUNICATIONS
An Automatic Zeroing Circuit RICHARD L. MASON, MEMBER, IEEE Abstract-A circuit to remove an offset from a signal is described. The circuit uses a simple digital memory to store the offset, and the output is the difference between this stored offset and the input signal. The drift is small, the bandwidth wide, and the input voltage may be obtained in digital form.
INTRODUCTION When an offset must be removed from a signal in which dc levels must be retained, one finds that it is convenient and often necessary to have a quick way to zero the output of the measurement system. For instance, in electro-oculargram studies, the offset voltage from the skin electrode drifts slowly with changes in body chemistry. This "source" drift must somehow be eliminated when recording the constant voltage levels corresponding to the subject's eye fixations. Usually, the offset is canceled by having the subject fixate a reference point at the beginning of a run and subtracting that reference level from all subsequent values (see Fig. 1). Thus, whenever the reference point is fixated, the system output is zero so that any offset-from the source or from instrumentation-is canceled in the output. This need to zero the system led to the circuit given here-a circuit which should be useful for any measurements in which the desired voltage levels are superimposed on an offset. The zeroing circuit is useful not only when obtaining data but also when reproducing or analyzing data stored on magnetic tape. It is particularly convenient if the zero marks are recorded along with the data. Then the recorded zero marks can be used to re-zero the data at the original locations, thus eliminating offsets in the record, reproduce, or any other amplifiers.
THE BASIC CIRCUIT Fig. 2 shows a version of the automatic zeroing circuit used when the input voltage is not required in digital form. This figure, which represents an operational circuit, will be used in the ensuing description of the automatic zeroing circuit. The A-D converter in Fig. 2 is used both to convert the input voltage to a digital number and to store that number. As long as the inhibit terminal is at logical one ( > + 2 V), the input voltage Ein is converted to digital form and varies. However, when inhibit is at zero, the output of the converter is constant and is that digital number corresponding to Ein at the instant inhibit changed from one to zero. This number corresponds to the offset voltage which will be removed. The A-D converter also inverts the data (since -5 V at Ein gives all ones at the digital output, and +5 V gives all zeros). Now consider the D-A converter in Fig. 2. The digital number is converted to an analog current in the D-A converter by internal resistors. The input voltage from the unity gain input amplifier is also converted to a current by the external resistors. The operational amplifier in the D-A converter sums the above currents and changes them to an output voltage which is the sum of the input voltage and the digital number stored in the A-D converter. Since the digital number is inverted, the output of the D-A converter is actually the difference between the input analog voltage and the digitally stored reference. Manuscript received December 3, 1973; revised August 1, 1974. The author is with the New London Laboratory, Naval Underwater Systems Center, New London, Conn. 06320.
Fig. 1. Establishing a zero reference. The circuit is useful both when making dc measurements and when reproducing recorded data.
Eol ZEROED VOLTAGE
(ANALOG)
MANUAL
INPUTI TAPE
INPUT
-i
ZERO
CONTROL LOGICAL I (>t2V) RUN ( LOGICAL 0 (i TRy8V) CHANGE TO NEW INPUTS ZERO REFERENCE J5
Fig. 2. Basic zeroing circuit. The unity gain amplifier and the A-D and D-A converters are required for each analog channel to be zeroed. The zero control provides the logic levels required for holding or changing reference levels. The relay amplifier energizes the relay only while zeroing. The zero reference is held while both zero control inputs are at logical 1; a logical 0 on either input changes all channels to a new zero reference.
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, SEPTEMBER 1975
428
A Note on Jogging on a Windy Day CHARLES P. HATSELL, MEMBER, IEEE Abstract-A minimum-time, fixed energy strategy for running a circular track on a windy day is derived which expresses velocity and acceleration as simple trigonometric functions of the runner's position on the track. Rather surprisingly, the strategy directs the runner to begin accelerating when the wind is directly in his face and decelerating with the wind directly at his back. O
(1) 8-BIT A-D CONVERTER (PHILBRICK 7110) (2) SN7475 OUAD LATCH (3) 8-BIT D-A CONVERTER (PHILBRICK 4021)
FROM ZERO
ONTROL OUT
Fig. 3. Modification to give both a digital output and zeroed analog output. The connection of the A-D inhibit terminal to +S V makes the A-D converter operate continuously. Latches are added to store the zero reference, and the zero control is connected to these latches.
The unity gain amplifier and relay shown at the input to the A-D converter in Fig. 2 are for isolation and, when zeroing, for smoothing the input. The relay is activated when the zero reference is being established so that the input is filtered by the 100-kQ., 10-,uF filter only while zeroing. If the input were not smoothed by this filter, the reference level would be determined not only by the desired dc level but also by the value of any noise at the input. The zero control circuit in Fig. 2 provides the proper logic levels to the A-D converter and the relay amplifier. When the manual zero and reproduce inputs are both at logical one (floating or greater than +2 V), the output of the control circuit is at logical zero and the reference is held. However, when either the manual zero or reproduce input to the control circuit goes to zero, the output of the control circuit goes to logical one and a new reference is established. If the data are being recorded, the zero marking voltage should also be recorded to show where zeroing occurred.
OBTAINING THE INPUT DATA IN DIGITAL FORM If the input data are required in digital form, the circuit of Fig. 2 must be modified. The required modifications, shown in Fig. 3, consist of reconnecting the A-D converter and adding latches. The inhibit terminal of the A-D converter is connected to +5 V so that the input voltage is continuously converted to digital form. The reference storage performed by the A-D converter is now accomplished by the latches. Latches are memory units whose output is the same as their input when the clock input is at logical one. When the clock input is at zero, the output of the latches is the input value at the time the clock changed state. Thus, by connecting the zero control to the latch clock input, one can store the output of the A-D converter for the zero reference. The modified circuit operates like the basic circuit, but now the input voltage is available in digital form without having the offset subtracted. ADJUSTMENTS The circuit requires two adjustments. A gain adjustment is made by applying a sine wave to the input and, with the zero activated, adjusting the gain until the output of the D-A converter is a straight line. The output is set to zero (or any desired offset) by adjusting the offset control with the zero activated. FREQUENCY RESPONSE The frequency response ofat e circuit is determined by the analog signal path and is affected only by the input and output operational amplifiers. Since the digital path provides the constant reference voltage, this path has no effect on the frequency response.
INTRODUCTION avid is aware that track running on a windy day Any jogger can be quite annoying, as he is alternately fighting and being aided by the wind. The question naturally arises as to whether or not there exists an optimal strategy for running a closed path under windy conditions. In this note a strategy is derived for a circular track. DEVELOPMENT Any question of optimality must be accompanied by stated criteria. In the case of track running it is natural to seek a strategy which minimizes lap time and simultaneously satisfies constraints on energy consumption and track geometry. In this paper it is required that a circular course be completed in minimum time with the expenditure of some fixed energy E. Although an oval track would more closely model most situations, circular geometry provides mathematical tractability and is insensitive to wind direction. For convenience, the wind is represented by a vector of magnitude W at 3frr/2 radians. The track has radius r and is run with velocity v(t) = rO(t), where 0(t) = dO/dt. The rate of energy expenditure by a runner on a circular track is given by E(t) = a++ 3V+ "yv(v + W COS 0)2 (1) where a is the resting metabolic rate; ,Bv is the power developed by the runner at velocity v in a windless situation; and 'yV(V + W COS 0)2 is the power developed to overcome wind resistance. Equation (1) summarizes the work of Pugh [1] who investigated 02 consumption of subjects running against the wind. For a lap time T, the total energy expenditure per lap is JT E(t) dt. EL= (2)
Hence, it is desired to minimize T subject to constraints of track geometry and fixed EL. The Lagrangian for this problem is given by L(0, 0, t) = 1 + X[t + r0 +yr0(0 + W cos 0)2] where v = rO has been substituted, and X is a Lagrange multiplier. A necessary condition for an extremum is the Euler-Lagrange equation, d/dt(aL/aG) - aL/aO = 0 (3) which yields, after rearranging terms and solving for the angular acceleration 0,
b
=
(W/r)(0)2
sin 0 30 + 2W/r cos 0
(4)
As angular acceleration is determined uniquely by angular Manuscript received September 9, 1974. The author is with the Department of Medicine, Wilford Hall United States Air Force Medical Center, Lackland Air Force Base, Tex.
COMMUNICATIONS
An Automatic Zeroing Circuit RICHARD L. MASON, MEMBER, IEEE Abstract-A circuit to remove an offset from a signal is described. The circuit uses a simple digital memory to store the offset, and the output is the difference between this stored offset and the input signal. The drift is small, the bandwidth wide, and the input voltage may be obtained in digital form.
INTRODUCTION When an offset must be removed from a signal in which dc levels must be retained, one finds that it is convenient and often necessary to have a quick way to zero the output of the measurement system. For instance, in electro-oculargram studies, the offset voltage from the skin electrode drifts slowly with changes in body chemistry. This "source" drift must somehow be eliminated when recording the constant voltage levels corresponding to the subject's eye fixations. Usually, the offset is canceled by having the subject fixate a reference point at the beginning of a run and subtracting that reference level from all subsequent values (see Fig. 1). Thus, whenever the reference point is fixated, the system output is zero so that any offset-from the source or from instrumentation-is canceled in the output. This need to zero the system led to the circuit given here-a circuit which should be useful for any measurements in which the desired voltage levels are superimposed on an offset. The zeroing circuit is useful not only when obtaining data but also when reproducing or analyzing data stored on magnetic tape. It is particularly convenient if the zero marks are recorded along with the data. Then the recorded zero marks can be used to re-zero the data at the original locations, thus eliminating offsets in the record, reproduce, or any other amplifiers.
THE BASIC CIRCUIT Fig. 2 shows a version of the automatic zeroing circuit used when the input voltage is not required in digital form. This figure, which represents an operational circuit, will be used in the ensuing description of the automatic zeroing circuit. The A-D converter in Fig. 2 is used both to convert the input voltage to a digital number and to store that number. As long as the inhibit terminal is at logical one ( > + 2 V), the input voltage Ein is converted to digital form and varies. However, when inhibit is at zero, the output of the converter is constant and is that digital number corresponding to Ein at the instant inhibit changed from one to zero. This number corresponds to the offset voltage which will be removed. The A-D converter also inverts the data (since -5 V at Ein gives all ones at the digital output, and +5 V gives all zeros). Now consider the D-A converter in Fig. 2. The digital number is converted to an analog current in the D-A converter by internal resistors. The input voltage from the unity gain input amplifier is also converted to a current by the external resistors. The operational amplifier in the D-A converter sums the above currents and changes them to an output voltage which is the sum of the input voltage and the digital number stored in the A-D converter. Since the digital number is inverted, the output of the D-A converter is actually the difference between the input analog voltage and the digitally stored reference. Manuscript received December 3, 1973; revised August 1, 1974. The author is with the New London Laboratory, Naval Underwater Systems Center, New London, Conn. 06320.
Fig. 1. Establishing a zero reference. The circuit is useful both when making dc measurements and when reproducing recorded data.
Eol ZEROED VOLTAGE
(ANALOG)
MANUAL
INPUTI TAPE
INPUT
-i
ZERO
CONTROL LOGICAL I (>t2V) RUN ( LOGICAL 0 (i TRy8V) CHANGE TO NEW INPUTS ZERO REFERENCE J5
Fig. 2. Basic zeroing circuit. The unity gain amplifier and the A-D and D-A converters are required for each analog channel to be zeroed. The zero control provides the logic levels required for holding or changing reference levels. The relay amplifier energizes the relay only while zeroing. The zero reference is held while both zero control inputs are at logical 1; a logical 0 on either input changes all channels to a new zero reference.
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, SEPTEMBER 1975
428
A Note on Jogging on a Windy Day CHARLES P. HATSELL, MEMBER, IEEE Abstract-A minimum-time, fixed energy strategy for running a circular track on a windy day is derived which expresses velocity and acceleration as simple trigonometric functions of the runner's position on the track. Rather surprisingly, the strategy directs the runner to begin accelerating when the wind is directly in his face and decelerating with the wind directly at his back. O
(1) 8-BIT A-D CONVERTER (PHILBRICK 7110) (2) SN7475 OUAD LATCH (3) 8-BIT D-A CONVERTER (PHILBRICK 4021)
FROM ZERO
ONTROL OUT
Fig. 3. Modification to give both a digital output and zeroed analog output. The connection of the A-D inhibit terminal to +S V makes the A-D converter operate continuously. Latches are added to store the zero reference, and the zero control is connected to these latches.
The unity gain amplifier and relay shown at the input to the A-D converter in Fig. 2 are for isolation and, when zeroing, for smoothing the input. The relay is activated when the zero reference is being established so that the input is filtered by the 100-kQ., 10-,uF filter only while zeroing. If the input were not smoothed by this filter, the reference level would be determined not only by the desired dc level but also by the value of any noise at the input. The zero control circuit in Fig. 2 provides the proper logic levels to the A-D converter and the relay amplifier. When the manual zero and reproduce inputs are both at logical one (floating or greater than +2 V), the output of the control circuit is at logical zero and the reference is held. However, when either the manual zero or reproduce input to the control circuit goes to zero, the output of the control circuit goes to logical one and a new reference is established. If the data are being recorded, the zero marking voltage should also be recorded to show where zeroing occurred.
OBTAINING THE INPUT DATA IN DIGITAL FORM If the input data are required in digital form, the circuit of Fig. 2 must be modified. The required modifications, shown in Fig. 3, consist of reconnecting the A-D converter and adding latches. The inhibit terminal of the A-D converter is connected to +5 V so that the input voltage is continuously converted to digital form. The reference storage performed by the A-D converter is now accomplished by the latches. Latches are memory units whose output is the same as their input when the clock input is at logical one. When the clock input is at zero, the output of the latches is the input value at the time the clock changed state. Thus, by connecting the zero control to the latch clock input, one can store the output of the A-D converter for the zero reference. The modified circuit operates like the basic circuit, but now the input voltage is available in digital form without having the offset subtracted. ADJUSTMENTS The circuit requires two adjustments. A gain adjustment is made by applying a sine wave to the input and, with the zero activated, adjusting the gain until the output of the D-A converter is a straight line. The output is set to zero (or any desired offset) by adjusting the offset control with the zero activated. FREQUENCY RESPONSE The frequency response ofat e circuit is determined by the analog signal path and is affected only by the input and output operational amplifiers. Since the digital path provides the constant reference voltage, this path has no effect on the frequency response.
INTRODUCTION avid is aware that track running on a windy day Any jogger can be quite annoying, as he is alternately fighting and being aided by the wind. The question naturally arises as to whether or not there exists an optimal strategy for running a closed path under windy conditions. In this note a strategy is derived for a circular track. DEVELOPMENT Any question of optimality must be accompanied by stated criteria. In the case of track running it is natural to seek a strategy which minimizes lap time and simultaneously satisfies constraints on energy consumption and track geometry. In this paper it is required that a circular course be completed in minimum time with the expenditure of some fixed energy E. Although an oval track would more closely model most situations, circular geometry provides mathematical tractability and is insensitive to wind direction. For convenience, the wind is represented by a vector of magnitude W at 3frr/2 radians. The track has radius r and is run with velocity v(t) = rO(t), where 0(t) = dO/dt. The rate of energy expenditure by a runner on a circular track is given by E(t) = a++ 3V+ "yv(v + W COS 0)2 (1) where a is the resting metabolic rate; ,Bv is the power developed by the runner at velocity v in a windless situation; and 'yV(V + W COS 0)2 is the power developed to overcome wind resistance. Equation (1) summarizes the work of Pugh [1] who investigated 02 consumption of subjects running against the wind. For a lap time T, the total energy expenditure per lap is JT E(t) dt. EL= (2)
Hence, it is desired to minimize T subject to constraints of track geometry and fixed EL. The Lagrangian for this problem is given by L(0, 0, t) = 1 + X[t + r0 +yr0(0 + W cos 0)2] where v = rO has been substituted, and X is a Lagrange multiplier. A necessary condition for an extremum is the Euler-Lagrange equation, d/dt(aL/aG) - aL/aO = 0 (3) which yields, after rearranging terms and solving for the angular acceleration 0,
b
=
(W/r)(0)2
sin 0 30 + 2W/r cos 0
(4)
As angular acceleration is determined uniquely by angular Manuscript received September 9, 1974. The author is with the Department of Medicine, Wilford Hall United States Air Force Medical Center, Lackland Air Force Base, Tex.
