APPLICATION NOTE 4798

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.

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 (

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.

Where V

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:

Where R

Where V

However, as V

And

Where V

R_{SENS_P(MAX)} |
= R_{SENS_P(NOM)} + its tolerance rating + R_{SENS_P(MIN)} |

= R_{SENS_P(NOM)} - its tolerance rating |

The short-circuit flag (active-low SC) will thus go low when the current is in the range between I

Where V

Considering that V

And

Where V

To determine the open-load detection window using a different sense resistor, first the given current levels must be converted to a voltage:

Then using the values calculated above, the typical value of the open-load current detection threshold calculates to:

Where V

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:

And

Where V

The worst-case open-load detection window lies between I

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:

VWhere AV is the (V_{OLT}(V) = I_{OLT}(A) × R_{SENS}(Ω) × A_{V}(V/V) + 0.133 × V_{REF}

RWhere V_{2}/R_{1}= V_{OLT}/(V_{REF}× (1 - V_{OLT}/V_{REF}))

The standard resistor values for R1 and R2 have now been defined. Next, considering the uncorrelated tolerances of V

And

Where R

At this point V

And

Where V

VAnd_{AOUT(MIN)}(V) = A_{OUT_Z(MIN)}(V) + A_{V(MIN)}(V/V) × R_{SENS(MIN)}(Ω) × I_{SENS}(A)

VWhere A_{AOUT(MAX)}(V) = A_{OUT_Z(MAX)}(V) + A_{V(MAX)}(V/V) × R_{SENS(MAX)}(Ω) × I_{SENS}(A)

Stated in other words, the sensed current produces a worst-case A

Taking the above worst-case voltage levels and using a microcontroller's software to calculate those voltages back to a current, one can calculate:

And

Where V

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 I

The current measurement tolerance, I

When using a resistor with a 1% tolerance, the maximum sense resistor that can be selected is:

As a 0.861Ω resistor is not available as a standard value, we select the next smaller value from the E96 series for R

Next, the typical current value for short-circuit detection can be calculated:

As previously shown, the minimum and maximum values for the short-circuit current-detection window lie between I

This allows us to derive the limits of the short-circuit current-detection window:

And

Analogous to the short-circuit current-detection window, the typical value of the current-limit range is:

Considering the tolerances, the minimum and maximum values for the current-limit range lie between I

And

Now for the MAX16913, the typical value for the open-load detection threshold is:

Including the tolerances, the minimum and maximum values are:

And

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:

Next we pick a standard resistor for R2 from the E96 series, 90.9kΩ (1%), and calculate its maximum value:

The minimum resistor value for the upper resistor of the divider is then:

The nominal value, assuming also a 1% tolerance, is:

The closest higher standard value to be selected with the same tolerance is R1 = 392kΩ. Considering also its tolerance, we calculate:

And the minimum value for R2 is:

Continuing with these values, the open-load threshold-voltage range is:

And

Then the worst-case current window for the open-load detection of the MAX16913A is:

And

To evaluate the analog output, A

VAnd_{AOUT(MIN)}(V) = A_{OUT_Z(MIN)}(V) + A_{V(MIN)}(V/V) × R_{SENS(MIN)}(Ω) × I_{SENS}(A) = 340mV + 12.87(V/V) × 0.837Ω × 100mA = 1.417V

VTaking 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:_{AOUT(MAX)}(V) = A_{OUT_Z(MAX)}(V) + A_{V(MAX)}(V/V) × R_{SENS(MAX)}(Ω) × I_{SENS}(A) = 460mV + 13.13(V/V) × 0.853Ω × 100mA = 1.58V

And

The worst-case tolerance of the measured current can then be up to:

*For more details on these calculations, see the data sheet for the MAX16913/MAX16913A.