Diode Resistance Levels and Temperature Effects

Diode resistance levels DC AC average AC resistance temperature effects ECE board exam infographic by PinoyBIX

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A resistor has one resistance value no matter where you measure it. A diode does not, because its I-V curve is not a straight line — its resistance changes depending on where you are on that curve and whether you are looking at a fixed operating point or a small signal swing around it. This post covers all three diode resistance levels — DC, AC, and average AC — plus how temperature shifts the numbers behind them.

This is Part 6 of the Semiconductor Diode Fundamentals ECE Board Exam Reviewer Series on PinoyBIX.org. Part 5 covered breakdown and the Zener region. This part shifts from voltage behavior to resistance behavior at a given operating point. If you are reviewing for the ECE or EE board exam or currently enrolled in Electronics 1, save this page.

📋 BOARD EXAM RELEVANCE

ECE (Electronics Engineer) — DC, AC, and average AC resistance calculations are a reliable source of numeric board exam items in Electronic Devices and Circuits. Expect 3 to 5 items requiring direct formula application, plus items testing the golden rule that lower current always means higher resistance across all three types.
EE (Electrical Engineer) — Appears with lower frequency, mostly limited to basic DC resistance and conceptual temperature effect questions.

Bottom line: ECE examinees must be fluent in all three resistance formulas and know which one a given problem calls for. EE examinees need DC resistance and general temperature behavior.

DC (Static) Resistance

DC resistance is measured at a single fixed operating point, called the Q-point, using the actual voltage and current values at that point. Graphically, it is the slope of a straight line drawn from the origin of the I-V curve to the Q-point itself.

KEY FORMULA — DC Resistance

$R_D = \dfrac{V_D}{I_D}$

AC (Dynamic) Resistance

AC resistance describes how the diode responds to a small signal riding on top of a DC operating point. Graphically, it is the slope of the tangent line to the I-V curve at the Q-point. At 25°C, this simplifies to a convenient formula using the thermal voltage constant of 26 mV.

KEY FORMULA — AC (Dynamic) Resistance

$r_d = \dfrac{26\text{ mV}}{I_D} \quad \text{(valid at } 25^\circ\text{C)}$

Total AC resistance in practice often adds the bulk resistance $r_B$ of the semiconductor material itself: $r'_d = r_d + r_B$ .

Average AC Resistance

Average AC resistance applies when a signal swings across a larger portion of the curve rather than staying close to a single point. It is calculated using two points that bracket the swing, forming a secant line instead of a tangent line.

KEY FORMULA — Average AC Resistance

$r_{av} = \dfrac{\Delta V_d}{\Delta I_d}$

The Golden Rule of Diode Resistance

All three resistance levels follow the same underlying rule: the lower the current through the diode, the higher its resistance, in every mode, always. This makes sense once you remember that a diode’s I-V curve is exponential in the forward region — steep near the top, shallow near the bottom.

KEY CONCEPT — Comparing the Three Resistance Types

At the same operating point, DC resistance ( $R_D$ ) is always larger than AC resistance ( $r_d$ ). Average AC resistance ( $r_{av}$ ) falls between whatever two points define the swing, and depends on how far apart those points are on the curve.

Temperature Effects Recap

Higher temperature lowers the forward voltage needed to reach a given current, and it raises the reverse saturation current $I_s$ , which roughly doubles for every 10°C rise, as covered in Post 4. The 26 mV thermal voltage constant used in the AC resistance formula is itself temperature-dependent, so the formula’s accuracy assumes operation near 25°C. Germanium shifts more per degree than silicon, which is part of why silicon remains the more thermally stable, industry-standard choice.

Worked Problems — Board Exam Type Questions

The following 10 problems are representative of actual ECE and EE board exam questions on diode resistance levels and temperature effects. Work each problem by hand before reading the solution.

Problem 1 — ECE Board Exam Type

A diode operates at a Q-point of $V_D = 0.7$ V, $I_D = 10$ mA. Find the DC resistance.

Given: $V_D = 0.7$ V, $I_D = 10$ mA

Find: $R_D$

Solution:

Step 1: Apply the DC resistance formula.

$R_D = \dfrac{V_D}{I_D} = \dfrac{0.7}{0.010} = 70\ \Omega$

✓ ANSWER: $R_D = 70\ \Omega$

Examiner note: DC resistance is simply Ohm’s law applied at a single fixed point on the curve.

Problem 2 — ECE Board Exam Type

The same diode from Problem 1 operates at 25°C. Find its AC (dynamic) resistance.

Given: $I_D = 10$ mA, $T = 25^\circ\text{C}$

Find: $r_d$

Solution:

Step 1: Apply the AC resistance formula.

$r_d = \dfrac{26\text{ mV}}{I_D} = \dfrac{26}{10} = 2.6\ \Omega$

✓ ANSWER: $r_d = 2.6\ \Omega$

Examiner note: Compare this to $R_D = 70\ \Omega$ from Problem 1 — AC resistance is always smaller than DC resistance at the same point.

Problem 3 — ECE Board Exam Type

A diode operates at $I_D = 5$ mA at 25°C. Find its AC resistance.

Given: $I_D = 5$ mA, $T = 25^\circ\text{C}$

Find: $r_d$

Solution:

Step 1: Apply the AC resistance formula.

$r_d = \dfrac{26\text{ mV}}{5\text{ mA}} = 5.2\ \Omega$

✓ ANSWER: $r_d = 5.2\ \Omega$

Examiner note: Compare this to Problem 2 — halving the current doubled the AC resistance, confirming the golden rule that lower current means higher resistance.

Problem 4 — ECE Board Exam Type

A diode’s I-V curve shows $\Delta V_d = 0.1$ V corresponding to $\Delta I_d = 20$ mA across a signal swing. Find the average AC resistance.

Given: $\Delta V_d = 0.1$ V, $\Delta I_d = 20$ mA

Find: $r_{av}$

Solution:

Step 1: Apply the average AC resistance formula.

$r_{av} = \dfrac{\Delta V_d}{\Delta I_d} = \dfrac{0.1}{0.020} = 5\ \Omega$

✓ ANSWER: $r_{av} = 5\ \Omega$

Examiner note: Average AC resistance requires two points on the curve, not one. If a problem only gives a single Q-point, you cannot compute $r_{av}$ .

Problem 5 — ECE Board Exam Type

At the same operating point, which is always larger: DC resistance $R_D$ or AC resistance $r_d$ ?

Given: Same Q-point comparison

Find: Which resistance is larger

Solution:

Step 1: $R_D$ is the slope of a line from the origin to the Q-point, while $r_d$ is the slope of the tangent line at that same point.

Step 2: Because the curve is exponential and concave, the origin-to-point slope is always steeper than the tangent slope at that point, making $R_D > r_d$ .

✓ ANSWER: $R_D$ is always larger than $r_d$ at the same point

Examiner note: Use this as a quick sanity check on your answers — if your computed $r_d$ comes out larger than $R_D$ at the same point, you have made an arithmetic error.

Problem 6 — ECE Board Exam Type

If the current through a diode is increased, what happens to its AC resistance $r_d$ ?

Given: Increasing diode current

Find: Effect on $r_d$

Solution:

Step 1: $r_d = 26\text{ mV}/I_D$ is inversely proportional to current.

Step 2: As $I_D$ increases, $r_d$ decreases.

✓ ANSWER: $r_d$ decreases

Examiner note: This is the golden rule in action — higher current always means lower resistance in every diode resistance mode.

Problem 7 — ECE Board Exam Type

Compare the AC resistance of a diode at $I_D = 1$ mA versus $I_D = 10$ mA, both at 25°C.

Given: $I_D = 1$ mA and $I_D = 10$ mA, $T = 25^\circ\text{C}$

Find: $r_d$ at each current, and the comparison

Solution:

Step 1: At $I_D = 1$ mA: $r_d = 26/1 = 26\ \Omega$

Step 2: At $I_D = 10$ mA: $r_d = 26/10 = 2.6\ \Omega$

✓ ANSWER: 26 Ω at 1 mA, 2.6 Ω at 10 mA — a tenfold increase in current produces a tenfold decrease in resistance

Examiner note: The AC resistance formula is a direct inverse proportion — multiplying current by 10 always divides resistance by 10.

Problem 8 — ECE Board Exam Type

A diode has $r_d = 2.6\ \Omega$ and a bulk resistance $r_B = 0.5\ \Omega$ . Find the total AC resistance.

Given: $r_d = 2.6\ \Omega$ , $r_B = 0.5\ \Omega$

Find: $r'_d$

Solution:

Step 1: Add the bulk resistance to the dynamic resistance.

$r'_d = r_d + r_B = 2.6 + 0.5 = 3.1\ \Omega$

✓ ANSWER: $r'_d = 3.1\ \Omega$

Examiner note: The bulk resistance accounts for the resistance of the actual semiconductor material and contact leads, and is often ignored in simplified problems unless explicitly given.

Problem 9 — ECE Board Exam Type

A diode has $I_s = 3\ \mu\text{A}$ at 25°C. Estimate $I_s$ at 35°C, assuming it roughly doubles every 10°C.

Given: $I_s = 3\ \mu\text{A}$ at 25°C, target 35°C

Find: Estimated $I_s$ at 35°C

Solution:

Step 1: The temperature rise is one full 10°C interval.

Step 2: Apply the doubling rule once.

$I_s(35^\circ\text{C}) = 3\ \mu\text{A} \times 2 = 6\ \mu\text{A}$

✓ ANSWER: $I_s \approx 6\ \mu\text{A}$ at 35°C

Examiner note: This same doubling relationship from Post 4 continues to apply here — resistance and leakage current calculations are closely linked through temperature.

Problem 10 — EE Board Exam Type

An EE board item describes a diode operating point where only a single voltage and current reading is available. Which resistance type can be computed: DC, AC, or average AC?

Given: Single voltage and current reading only

Find: Which resistance type is computable

Solution:

Step 1: DC resistance only requires one voltage and current pair at a single point.

Step 2: AC resistance requires either the 26 mV formula with a known current, or a slope measurement; average AC resistance requires two points.

✓ ANSWER: Only DC resistance can be directly computed from a single voltage and current reading

Examiner note: Recognizing what data a formula actually requires is as important as knowing the formula itself.

Common Mistakes and Examiner Traps

❌ Mistake	✅ Correction
Using the rd formula when RD is asked for	Check which resistance type the problem specifies before selecting a formula — $R_D$ uses actual values at one point, $r_d$ uses the 26 mV constant.
Forgetting 26 mV is only valid near 25°C	Confirm the operating temperature before applying the standard $r_d$ formula without adjustment.
Mixing up $\Delta V_d / \Delta I_d$ direction in $r_{av}$	Keep voltage change over current change, using two clearly defined points on the curve.
Using the wrong current value inside the $r_d$ formula	Use the DC bias current $I_D$ at the Q-point, not a peak or average signal current, unless the problem specifies otherwise.
Ignoring bulk resistance in total AC resistance	Add $r_B$ when given: $r'_d = r_d + r_B$ .

Board Exam Quick Tips

Lower current through the diode means higher resistance, always — in DC, AC, or average AC mode. This one rule anchors every resistance question.
The 26 mV constant in $r_d = 26\text{ mV}/I_D$ only holds at 25°C. If a problem states a different temperature, do not blindly plug in 26 mV.
DC resistance ( $R_D$ ) is always greater than AC resistance ( $r_d$ ) at the same operating point — use this as a quick sanity check on your answer.
Average AC resistance needs two points on the curve, not one. If the problem only gives a single Q-point, you cannot compute $r_{av}$ .
Reverse saturation current roughly doubles every 10°C rise in temperature — memorize this exact multiplier; it shows up in numeric board items.

Frequently Asked Questions

Q1. Why does a diode need three different resistance formulas instead of just one?

Because its I-V curve is nonlinear. A single fixed value cannot describe behavior across the whole curve, so DC resistance describes a bias point, AC resistance describes a small-signal response, and average AC resistance describes a larger signal swing.

Q2. Can $r_d$ ever be larger than $R_D$ at the same point?

No, under standard diode curve behavior. $R_D$ is the slope from the origin, always steeper than the tangent slope $r_d$ at the same point on an exponential curve.

Q3. Is the 26 mV value fixed for every diode?

It is a thermal voltage approximation valid near room temperature (25°C) for silicon diodes, derived from fundamental physical constants. It shifts with actual operating temperature.

Q4. When would an engineer use average AC resistance instead of dynamic resistance?

When the signal swing across the diode is large enough that a single tangent-line approximation at one point would not accurately represent the diode’s behavior across the whole swing.

Q5. Does bulk resistance change with current the way $r_d$ does?

No. Bulk resistance $r_B$ is treated as a relatively fixed physical property of the semiconductor material and contacts, unlike $r_d$ , which depends directly on the bias current.

What Is Next

Now that you can compute all three diode resistance levels, the next post ties everything from this series together into three formal approximation levels used to model a diode in circuit analysis — ideal, simplified, and piecewise-linear.

→ Continue to Post 7 — Diode Equivalent Circuits and Approximation Levels

→ Back to the Semiconductor Diode Fundamentals Series Index

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Diode Resistance Levels and Temperature Effects | ECE Board Reviewer

DC (Static) Resistance

AC (Dynamic) Resistance

Average AC Resistance

The Golden Rule of Diode Resistance

Temperature Effects Recap