# What is the relationship between DC resistance and AC resistance of a diode?

## Introduction

Diodes are semiconductor devices that allow current to flow in only one direction. They have unique electrical characteristics that make them useful for a variety of applications such as rectification, switching, clamping, etc. One important parameter that defines the behavior of a diode is its resistance. However, the resistance is not constant and varies with the type of current – Direct Current (DC) or Alternating Current (AC). In this article, we will explore the difference between DC and AC resistance of a diode and the relationship between the two.

## DC Resistance

The DC resistance of a diode refers to the resistance offered by the diode to a direct current. It is the ratio of the applied DC voltage across the diode to the resulting DC current through it. Some key points regarding DC resistance:

• DC resistance arises from the bulk resistance of the semiconductor material used to make the diode. It is relatively low, typically just a few ohms.
• DC resistance stays fairly constant until the diode starts conducting current in the forward biased condition.
• Once the diode starts conducting, the DC resistance drops exponentially as the current increases.
• DC resistance is low in forward bias and very high (ideally infinite) in reverse bias.
• DC resistance can be derived from the diode’s I-V curve and is equal to the inverse slope of the curve in the linear region before the diode turns on.

DC Resistance vs Forward Current curve for a diode showing low constant resistance initially followed by exponential decrease upon conduction.

## AC Resistance

AC resistance refers to the resistance offered by a diode to alternating current. It arises primarily due to the junction capacitance of a diode and differs significantly from DC resistance. Some key points:

• AC resistance is frequency dependent and varies with the frequency of the AC signal applied.
• At very low frequencies, AC resistance is high and nearly equal to DC resistance in reverse bias.
• As frequency increases, AC resistance starts decreasing due to charging and discharging of junction capacitance.
• The junction capacitance provides a low reactance path for AC at higher frequencies. Hence, AC resistance decreases.
• At very high frequencies, AC resistance approaches a minimum value known as dynamic resistance.

Variation of AC Resistance with frequency for a diode showing decrease with increase in frequency.

## Relationship between DC and AC Resistance

From the characteristics described above, we can summarize the relationship between DC and AC resistance as follows:

• At very low frequencies, AC resistance ≈ DC resistance in reverse bias
• As frequency increases, AC resistance decreases while DC resistance remains unchanged
• DC resistance represents a lower limit for AC resistance but AC resistance can never fall below DC resistance
• At very high frequencies, AC resistance approaches dynamic resistance which is higher than DC resistance
• DC resistance is determined by the bulk resistance of the diode material
• AC resistance depends on frequency and junction capacitance along with bulk resistance

Therefore, we can conclude that AC resistance is always greater than or equal to DC resistance for a diode. But the exact relationship varies depending on the frequency. The AC resistance equals the DC value only under static conditions at low frequencies. As frequency increases, the AC resistance starts decreasing due to capacitive effects while the DC resistance remains constant.

## What causes the difference between DC and AC resistances?

The key factors that cause the DC and AC resistances to be different are:

### 1. Junction Capacitance

• Every PN junction has an inherent junction capacitance which depends on the area of the junction, doping levels and voltage applied.
• In reverse bias, the depletion region at the junction acts as the dielectric of a parallel plate capacitor causing capacitance.
• Under AC, this capacitance provides a reactive path for the current to flow by charging and discharging.
• Hence, AC resistance decreases with increase in frequency due to capacitive reactance.

### 2. Minority Carrier Injection

• Under DC, only majority carriers contribute to conduction which depends on the bulk resistance.
• But in AC, minority carriers also get injected into the junction when it is forward biased during one half cycle.
• These extra carriers increase the conductivity and lower the dynamic resistance under AC conditions.

### 3. Temperature Effects

• DC resistance has a positive temperature coefficient – increases with temperature due to higher lattice vibrations.
• But AC resistance and capacitance are negatively affected by temperature rise.
• So heating causes DC resistance to increase but AC resistance decreases due to reduced capacitive reactance.

### 4. Non-linear I-V Characteristics

• The diode does not follow Ohm’s law. Instead it has an exponential I-V relationship in forward bias.
• So AC resistance becomes dependent on the operating point unlike the DC case.
• Significant non-linearity causes DC and AC resistances to diverge.

### 5. Transit Time Effects

• At high frequencies, the diode’s transit time for carriers starts affecting the AC resistance.
• Transit time acts as a small inductance, thereby increasing impedance.
• Thus transit time effects also contribute to the difference between DC and AC resistances.

## How are DC and AC resistances specified in diode datasheets?

Diode datasheets often provide the following resistance specifications:

• DC resistances are specified at a particular forward current and reverse voltage.
• Dynamic resistance is specified at a test frequency, usually 1 MHz.
• Junction capacitance values are provided as a function of reverse voltage.
• Forward resistance is represented by slope of forward I-V curve.
• Temperature dependence of resistances is also specified.
• Switching times and transit times indicate high frequency limitations.

By combining the DC resistance, junction capacitance and other parameters, the AC resistance at different frequencies can be estimated.

## Applications exploiting the DC and AC resistance properties

The difference between the DC and AC resistances of a diode is useful for the following applications:

### Rectification

• Low DC resistance in forward bias allows high DC currents for rectification.
• High AC resistance in reverse bias blocks reverse AC voltages.

### Switching and Clamping

• Fast switching between low and high resistance states allows using diode as switch.
• Varying AC resistance helps in waveform clamping and shaping.

• Variation of AC resistance with frequency is useful for detection of RF signals.
• Diode resistance matches to load at signal frequency for good impedance matching.

### Reverse Leakage Control

• High DC resistance in reverse bias minimizes reverse saturation current.
• This reduces leakage and improves performance.

### Temperature Sensing

• DC resistance change with temperature is utilized for sensing.
• AC resistance change is relatively lower, hence does not affect temperature sensitivity.

## Conclusion

To summarize, DC and AC resistances are two different diode parameters that are related but not equal in magnitude. DC resistance represents the static bulk resistance while AC resistance is frequency dependent due to capacitive effects. AC resistance equals DC resistance only at very low frequencies and starts decreasing as frequency rises. The difference arises due to factors like junction capacitance, minority carrier injection, temperature effects and transit time. Diode datasheets specify DC resistances along with parameters like capacitance and transit time to allow estimating AC resistance. The variation between DC and AC resistances is exploited in applications like rectification, switching, clamping, RF detection and temperature sensing. Proper understanding of the relationship between the two resistances is therefore important for selecting the right diode for different applications.

### Q1. Why does AC resistance decrease with increase in frequency?

Ans: AC resistance decreases with increase in frequency because of the junction capacitance of the diode. At higher frequencies, the capacitive reactance XC becomes low, providing an alternate lower resistance path for AC current to flow through capacitance by charging and discharging effect.

### Q2. Is AC resistance affected by temperature?

Ans: Yes, AC resistance is affected by temperature. Increase in temperature causes the junction capacitance to decrease due to increase in intrinsic carrier concentration. This causes the AC resistance to increase with temperature.

### Q3. Is AC resistance higher or lower than DC resistance?

Ans: AC resistance is always higher than or equal to DC resistance. It equals DC resistance only at very low frequencies when capacitive effects are negligible. At higher frequencies, AC resistance becomes lower than DC resistance due to capacitive reactance but never falls below the DC resistance value.

### Q4. Does a diode follow Ohm’s law?

Ans: No, a diode does not follow Ohm’s law. It has an exponential I-V relationship in forward bias due to its PN junction properties. This non-linear V-I curve causes the AC resistance to become dependent on the operating point.

### Q5. Why does transit time affect AC resistance?

Ans: At high frequencies, the diode’s transit time for charge carriers starts affecting the AC resistance. Transit time acts as a small inductance that increases impedance and hence increases AC resistance at very high frequencies.

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