APPLICATION NOTE 4798

How to Calculate the Operating Windows for a Remote Antenna Current-Sense Amplifier and Switch

By: Robert Regensburger

Abstract: This application note helps designers choose the correct external components to ensure that automobile antenna-detection circuitry meets performance objectives. A calculator details how to specify the critical external components for the MAX16913/MAX16913A remote antenna current-sense amplifiers and switches. The calculator also determines the device's operational windows and analog output voltage accuracy. An example calculation is given.

Introduction

The MAX16913/MAX16913A (Figure 1) are precision current-sense amplifiers (CSAs) and switches that provide phantom power to remote radio antennas in automotive applications. In addition, they provide short-circuit protection, current-limit protection, and open-load detection. To ensure that their antenna detection circuitry meets performance objectives, the design engineer must choose the correct external components for a design.

When working with CSAs and switches for antenna applications, the designer must often determine the operational windows for an open load, normal operation, a short circuit, and current limiting (Figure 2). In addition, the accuracy of the CSA's analog output voltage must also be verified.

Figure 1. Typical operating circuit of the MAX16913A remote antenna CSA and switch.
Figure 1. Typical operating circuit of the MAX16913A remote antenna CSA and switch.

Figure 2. Operation ranges for these CSAs.
Figure 2. Operation ranges for these CSAs.

This application note presents a calculator that shows how to determine the proper sense resistor and the resistor-divider for setting the open-load threshold (detection range) tolerance. It considers the tolerances of both the external components and the MAX16913/MAX16913A, and then calculates the appropriate tolerance window ranges for optimal performance. The calculator is available here, and an example calculation follows.

Calculate the Required Sense Resistor

Ideally the maximum operating current develops the full-scale sense voltage across the current-sense resistor, RSENS (Figure 1). Calculate the maximum value for RSENS so that the differential voltage across IN and SENS does not exceed the minimum full-scale sense voltage (87mV)*:
Equation 1.
Where VDIFF(MIN) = VIN - VSENSE = 87mV (min) at the maximum guaranteed output current, ILOAD(FULL-SCALE) (Figure 2).

However, resistors always have tolerances, so the actual resistor value can be higher by its tolerance rating, thus causing the device to detect a short circuit too early. After considering the resistor's tolerance rating, the nominal maximum resistor value can be calculated:
Equation 2.
Where RSENS(MAX) is the maximum sense resistor calculated above, and RSENS-TOLERANCE is the tolerance rating of the resistor. Remember that exact values for the calculated sense resistor may not be available. If that is the case, choose the closest smaller value for RSENS(MAX)(NOM) and use that to calculate RSENS_P(NOM). Alternatively serial or parallel combinations of standard resistors can be used to attain the optimal sense resistor.

Calculate the Short-Circuit Current-Detection Window

The nominal sense resistor has been chosen. Now the typical current through the sense resistor, when a short circuit is detected, can be calculated as follows:
Equation 3.
Where VSC(TYP) is the typical value of the short-circuit voltage threshold (100mV)* and RSENS_P(NOM) is the sense resistor selected above.

However, as VSC and RSENS have uncorrelated tolerances (i.e., have minimum and maximum values that vary independently of each other), an additional error has to be considered. So the worst-case short-circuit, current-detection window is:
Equation 4.
And
Equation 5.
Where VSC(MIN) is the minimum value of the short-circuit voltage threshold (87mV)* and VSC(MAX) is the maximum value (110mV).* Therefore:

RSENS_P(MAX) = RSENS_P(NOM) + its tolerance rating + RSENS_P(MIN)
  = RSENS_P(NOM) - its tolerance rating

The short-circuit flag (active-low SC) will thus go low when the current is in the range between ISC(MIN) and ISC(MAX).

Calculate the Current-Limit Range

Analogous to the short-circuit current-detection window, the current-limit range is typically:
Equation 6.
Where VLIM(TYP) is the typical value of the current-limit threshold voltage between IN and SENS (200mV),* and RSENS_P(NOM) is the sense resistor selected.

Considering that VLIM and RSENS have uncorrelated tolerances, the worst-case current-limit range through the sense resistor can be calculated:
Equation 7.
And
Equation 8.
Where VLIM(MIN) is the minimum value of the voltage between IN and SENS (173mV),* and VLIM(MAX) is the maximum value (225mV).*

Calculate the Open-Load Detection Window

This procedure differs for the MAX16913 and MAX16913A.

For the MAX16913

The open-load detection threshold (active-low OL) for the MAX16913 is set internally to VOLT = 0.66V.* The associated current range using a 1Ω resistor is specified in the data sheet as 10mA (min), 20mA (typ), and 30mA (max). These values include the tolerance of the open-load comparator, the gain amplifier, and the external sense resistor (1Ω).

To determine the open-load detection window using a different sense resistor, first the given current levels must be converted to a voltage:
Equation 9.
Then using the values calculated above, the typical value of the open-load current detection threshold calculates to:
Equation 10.
Where VOLT(TYP) is the typical value of the open-load detection-threshold voltage calculated above, and RSENS_P(NOM) is the sense resistor selected.

Considering also the tolerances of the open-load current threshold and the tolerance of the sense resistor, then the current range for open-load detection calculates to:
Equation 11.
And
Equation 12.
Where VOLT(MIN) and VOLT(MAX) are the minimum and maximum values of the open-load detection-threshold voltage; RSENS_P(MIN) and RSENS_P(MAX) are the minimum and maximum values of the sense resistor calculated above.

The worst-case open-load detection window lies between IOL(MIN) and IOL(MAX).

For the MAX16913A

The open-load threshold for the MAX16913A can be adjusted externally with a resistor-divider between REF, OLT, and GND. Therefore, the first task is to specify the external resistor-divider.

Specify the External Resistor-Divider
To begin, choose the voltage needed on the OLT pin to set the desired nominal OL threshold (at the OLT pin, Figure 1) using the following formula:
VOLT(V) = IOLT(A) × RSENS(Ω) × AV(V/V) + 0.133 × VREF
Where AV is the (VIN - VSENS) to VAOUT gain (13V/V) and VREF is the REF pin voltage (3V).* The ratio of the external resistors on the OLT pin can then be calculated using the following equation:
R2/R1 = VOLT/(VREF × (1 - VOLT/VREF))
Where VREF is the voltage on the REF pin (3V). An arbitrary standard value can now be chosen for R1 or R2, and the other resistor value can then be calculated (Figure 1). However, ensure that the impedance of the resistor-divider does not load the internal reference voltage excessively.

Determine the Open-Load Threshold-Voltage Range
The standard resistor values for R1 and R2 have now been defined. Next, considering the uncorrelated tolerances of VREF and the resistors R1 and R2, the worst-case voltage range for the open-load pin, VOLTw, can be calculated:
Equation 13.
And
Equation 14.
Where R2(MIN) is the nominal value of R2 minus its tolerance value. This can be restated as R2(MIN) = R2 - (R2 × (R2TOL[%]/100%)) and R1(MAX) is the nominal value of R1 plus the tolerance.

Determine the Worst-Case, Open-Load Current-Detection Window
At this point VOLTw(MIN) and VOLTw(MAX) have been calculated. Now taking into consideration the tolerances of the REF output voltage, VREF, the sense resistor, RSENS_P(NOM), and the gain, AV, the worst-case current window when open load is detected (active-low OL) can be calculated:
Equation 15.
And
Equation 16.
Where VOLTw(MIN), VOLTw(MAX), RSENS_P(MIN), and RSENS_P(MAX) have been calculated above; AV is the (VIN - VSENS) to VAOUT gain which has minimum and maximum values of 12.87 and 13.13, respectively*; and VREF(MIN) and VREF(MAX) are the minimum and maximum values of the REF pin voltage (2.7V and 3.3V).*

Evaluate the Current Through RSENS by Measuring Voltage on AOUT

AOUT Accuracy

With a given sense resistor, RSENS, and a defined current through it, ISENS, then the worst-case range of voltage values measured at the current-sense amplifier's output, AOUT (e.g., a microcontroller's analog-to-digital converter (ADC)), can now be calculated. Consider also the uncorrelated tolerances of AOUT_Z and the sense resistor, RSENS. Therefore:
VAOUT(MIN)(V) = AOUT_Z(MIN)(V) + AV(MIN)(V/V) × RSENS(MIN)(Ω) × ISENS(A)
And
VAOUT(MAX)(V) = AOUT_Z(MAX)(V) + AV(MAX)(V/V) × RSENS(MAX)(Ω) × ISENS(A)
Where AV(MIN) is 12.87V and AV(MAX) is 13.13V;* and AOUT_Z(MIN) and AOUT_Z(MAX) are the minimum and maximum values of the AOUT zero-current output voltage (340mV)* (460mV);* and RSENS(MIN) and RSENS(MAX) are the sense resistor plus/minus its tolerance.

Stated in other words, the sensed current produces a worst-case AOUT voltage variation between VAOUT(MIN) and VAOUT(MAX).

Taking the above worst-case voltage levels and using a microcontroller's software to calculate those voltages back to a current, one can calculate:
Equation 17.
And
Equation 18.
Where VAOUT(MIN) and VAOUT(MAX) have been calculated above; AV is the (VIN - VSENS) to VAOUT gain (13V/V);* AOUT_Z(TYP) is the typical value of the AOUT zero-current output voltage (400mV);* and RSENS is the nominal value of the sense resistor.

Thus when the analog output voltage is used to measure a certain current through the sense resistor, the microcontroller's ADC gives a current value between IEVALUATED(MIN) and IEVALUATED(MAX).

The current measurement tolerance, ITOL, is:
Equation 19.

Example Calculations

For these example calculations we assume an antenna phantom supply application where the upper end of the normal operation window (ILOAD(FULL-SCALE)) is at 100mA. Then the maximum value of the sense resistor required is:
Equation 20.
When using a resistor with a 1% tolerance, the maximum sense resistor that can be selected is:
Equation 21.
As a 0.861Ω resistor is not available as a standard value, we select the next smaller value from the E96 series for RSENS-P(NOM) = 0.845Ω. We use this value for our subsequent calculations.

Next, the typical current value for short-circuit detection can be calculated:
Equation 22.
As previously shown, the minimum and maximum values for the short-circuit current-detection window lie between ISC(MIN) and ISC(MAX). To calculate these values, we first need the minimum and maximum values of the selected sense resistor.

Equation 23.
This allows us to derive the limits of the short-circuit current-detection window:
Equation 24.
And
Equation 25.
Analogous to the short-circuit current-detection window, the typical value of the current-limit range is:
Equation 26.
Considering the tolerances, the minimum and maximum values for the current-limit range lie between ILIM(MIN) and ILIM(MAX):
Equation 27.
And
Equation 28.
Now for the MAX16913, the typical value for the open-load detection threshold is:
Equation 29.
Including the tolerances, the minimum and maximum values are:
Equation 30.
And
Equation 31.
Turning now to the MAX16913A, we assume an application where the maximum current value of the open-load detection window is at 30mA. Therefore, the maximum voltage value for the center point of the resistor-divider is:
Equation 32.
Next we pick a standard resistor for R2 from the E96 series, 90.9kΩ (1%), and calculate its maximum value:
Equation 33.
The minimum resistor value for the upper resistor of the divider is then:
Equation 34.
The nominal value, assuming also a 1% tolerance, is:
Equation 35.
The closest higher standard value to be selected with the same tolerance is R1 = 392kΩ. Considering also its tolerance, we calculate:
Equation 36.
And the minimum value for R2 is:
Equation 37.
Continuing with these values, the open-load threshold-voltage range is:
Equation 38.
And
Equation 39.
Then the worst-case current window for the open-load detection of the MAX16913A is:
Equation 40.
And
Equation 41.
To evaluate the analog output, AOUT, accuracy, we assume the same sense resistor selected above (0.845Ω) and evaluate the accuracy at a load current of 100mA. At this current, the minimum and maximum values of the AOUT voltage are between:
VAOUT(MIN)(V) = AOUT_Z(MIN)(V) + AV(MIN)(V/V) × RSENS(MIN)(Ω) × ISENS(A) = 340mV + 12.87(V/V) × 0.837Ω × 100mA = 1.417V
And
VAOUT(MAX)(V) = AOUT_Z(MAX)(V) + AV(MAX)(V/V) × RSENS(MAX)(Ω) × ISENS(A) = 460mV + 13.13(V/V) × 0.853Ω × 100mA = 1.58V
Taking these voltages and calculating back as the microcontroller's software would do (i.e., taking the typical values from the data sheet), we derive an evaluated current between:
Equation 44.
And
Equation 45.
The worst-case tolerance of the measured current can then be up to:
Equation 46.
*For more details on these calculations, see the data sheet for the MAX16913/MAX16913A.