science

Leapfrog filter

Leapfrog filter is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Leapfrog filter rather than just read about it. In short: A leapfrog filter is a type of active circuit electronic filter that simulates a passive electronic ladder filter. Other names for this type of filter are active-ladder or multiple feedback filter.

Key takeaways

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

Reference excerpt

A leapfrog filter is a type of active circuit electronic filter that simulates a passive electronic ladder filter. Other names for this type of filter are active-ladder or multiple feedback filter. The arrangement of feedback loops in the signal flow-graph of the simulated ladder filter inspired the name leapfrog filter, which was coined by Girling and Good. The leapfrog filter maintains the low component sensitivity of the passive ladder filter that it simulates.

Synthesis

The definition and synthesis of leapfrog filters is described by Temes & LaPatra, Sedra & Brackett, Chen and Wait, Huelsman & Korn. Synthesis of leapfrog filters typically includes the following steps:

Determine a prototype passive ladder filter that has the desired frequency response. Usually a doubly terminated prototype is used. Write the equations relating element current to voltage across the element in a form suitable for expression as a signal-flow graph. Draw the signal-flow graph. The nodes of the signal-flow graph will include both voltages and currents. The branch gains will include impedances and admittances. Convert all nodes of the signal-flow graph to voltages and all impedances to dimensionless transmittances. This is accomplished by dividing all impedance elements by R, an arbitrary resistance and multiplying all admittance elements by R. This scaling does not change the frequency response. Manipulate the signal-flow graph so that the gains feeding each summing node have the same signs. This is done as an implementation convenience. At the completion of this step, typically, all the feedback gains in the signal-flow graph will be +1 and the signs of the gain blocks in the forward path will alternate. As a result, some of the nodes, including the main output, may have a 180° phase inversion. This is usually of no consequence. The gain blocks are implemented with active filters and interconnected as indicated by the signal-flow graph. Often, state variable filters are used for the gain blocks. The final circuit usually has more components than the prototype passive filter. This means the final circuit has degrees of freedom which can be chosen to optimize the circuit for dynamic range and for practical component values.

Examples

Generic filter

The design starts out with a known ladder filter of one of the typologies shown in the previous figure. Usually, all the elements of the ladder filter are lossless except the first and the last which are lossy. Using a four element voltage input, voltage output ladder filter as an example, the equations that relate the element voltages and currents are as follows:

I 1 = ( V 0 − V 2 ) Y 1 {\displaystyle I_{1}=(V_{0}-V_{2})\mathrm {Y_{1}} }

V 2 = ( I 1 − I 3 ) Z 2 {\displaystyle V_{2}=(I_{1}-I_{3})\mathrm {Z_{2}} }

I 3 = ( V 2 − V 4 ) Y 3 {\displaystyle I_{3}=(V_{2}-V_{4})\mathrm {Y_{3}} }

V 4 = ( I 3 ) Z 4 {\displaystyle V_{4}=(I_{3})\mathrm {Z_{4}} }

The signal-flow graph for these equations are shown in the second figure to the right. The arrangement of feedback loops in the signal flow-graph inspired the name leapfrog filter. The signal flow graph is manipulated to convert all current nodes into voltage nodes and all the impedances and admittances into dimensionless transmittances. This is equivalent to manipulating the equations either by multiplying both sides by R or by multiplying one side by R/R and distributing the R terms across the subtraction operation. This manipulation changes the equations as follows:

V 1 = ( V 0 − V 2 ) H 1 {\displaystyle V_{1}=(V_{0}-V_{2})\mathrm {H_{1}} }

V 2 = ( V 1 − V 3 ) H 2 {\displaystyle V_{2}=(V_{1}-V_{3})\mathrm {H_{2}} }

V 3 = ( V 2 − V 4 ) H 3 {\displaystyle V_{3}=(V_{2}-V_{4})\mathrm {H_{3}} }

V 4 = ( V 3 ) H 4 {\displaystyle V_{4}=(V_{3})\mathrm {H_{4}} }

… excerpt ends here. Continue reading the full article.

Illustrations

Worked examples

Example 1 — a first encounter with Leapfrog filter

Start with the simplest possible case. Write down what Leapfrog filter claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, 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 Leapfrog filter 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 Leapfrog filter 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 Leapfrog filter

In research: Leapfrog filter appears in science 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 Leapfrog filter 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: Leapfrog filter is common in secondary-school and first-year university syllabi. It links to neighbouring topics Linear filters, Signal processing filter, so understanding it makes those chapters shorter.
In everyday life: Look for Leapfrog filter 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.

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How to study Leapfrog filter in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Leapfrog filter 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 Leapfrog filter out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Leapfrog filter in simple terms?

A leapfrog filter is a type of active circuit electronic filter that simulates a passive electronic ladder filter. Other names for this type of filter are active-ladder or multiple feedback filter.

Why does Leapfrog filter matter?

Because it connects several science 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 Leapfrog filter?

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 Leapfrog filter.