Miller effect

Key takeaways

Miller effect belongs to engineering; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Miller effect to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Miller effect from memory before moving on to harder problems.

Reference excerpt

In electronics, the Miller effect (named after its discoverer John Milton Miller) accounts for the increase in the equivalent input capacitance of an inverting voltage amplifier due to amplification of the effect of capacitance between the amplifier's input and output terminals, and is given by

C M = C ( 1 + A v ) , {\displaystyle C_{\text{M}}=C(1+A_{v}),}

where − A v {\displaystyle -A_{v}} is the voltage gain of the inverting amplifier ( A v {\displaystyle A_{v}} positive), and C {\displaystyle C} is the feedback capacitance. Although the term Miller effect normally refers to capacitance, any impedance connected between the input and another node exhibiting gain can modify the amplifier input impedance via this effect. These properties of the Miller effect are generalized in the Miller theorem. The Miller capacitance due to undesired parasitic capacitance between the output and input of active devices like transistors and vacuum tubes is a major factor limiting their gain at high frequencies.

History When Miller published his work in 1919, he was working on vacuum tube triodes. The same analysis applies to modern devices such as bipolar junction and field-effect transistors.

Derivation

Consider a circuit of an ideal inverting voltage amplifier of gain − A v {\displaystyle -A_{v}} with an impedance Z {\displaystyle Z} connected between its input and output nodes. The output voltage is therefore V o = − A v V i {\displaystyle V_{o}=-A_{v}V_{i}} . Assuming that the amplifier input draws no current, all of the input current flows through Z {\displaystyle Z} , and is therefore given by

I i = V i − V o Z = V i ( 1 + A v ) Z {\displaystyle I_{i}={\frac {V_{i}-V_{o}}{Z}}={\frac {V_{i}(1+A_{v})}{Z}}} . The input impedance of the circuit is

Z i n = V i I i = Z 1 + A v {\displaystyle Z_{in}={\frac {V_{i}}{I_{i}}}={\frac {Z}{1+A_{v}}}} . In the Laplace domain (where s {\displaystyle s} represents complex frequency), if Z {\displaystyle Z} consists of just a capacitor forming a complex impedance Z = 1 s C {\displaystyle Z={\frac {1}{sC}}} , then the circuit's resulting input impedance will be equivalent to that of a larger capacitance C M {\displaystyle C_{M}} :

Z i n = 1 s C ( 1 + A v ) = 1 s C M w h e r e C M = C ( 1 + A v ) {\displaystyle Z_{in}={\frac {1}{sC(1+A_{v})}}={\frac {1}{sC_{M}}}\quad \mathrm {where} \quad C_{M}=C(1+A_{v})} . This Miller capacitance C M {\displaystyle C_{M}} is the physical capacitance C {\displaystyle C} multiplied by the factor ( 1 + A v ) {\displaystyle (1+A_{v})} .

… excerpt ends here. Continue reading the full article.

Illustrations

Worked examples

Example 1 — a first encounter with Miller effect

Start with the simplest possible case. Write down what Miller effect claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In engineering, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Miller effect before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Miller effect ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Miller effect

In research: Miller effect appears in engineering research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Miller effect in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Miller effect is common in secondary-school and first-year university syllabi. It links to neighbouring topics Analog circuits, Electrical engineering, Electronic design, so understanding it makes those chapters shorter.
In everyday life: Look for Miller effect outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

How to study Miller effect in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Miller effect means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Miller effect out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Miller effect in simple terms?

In electronics, the Miller effect (named after its discoverer John Milton Miller) accounts for the increase in the equivalent input capacitance of an inverting voltage amplifier due to amplification of the effect of capacitance between the amplifier's input and output terminals, and is given by C M…

Why does Miller effect matter?

Because it connects several engineering ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Miller effect?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Miller effect.