The basic and important theory that modern electronics are completely based on is Amplification. And the device which is utilized for the purpose of amplification is Amplifier. In the concept of amplifiers, the first practical device that was used is a triode vacuum tube in the year 1906 and this invention led to the discovery of amplifiers in 1912. And now, there are many classifications in amplifiers such as single tuned, double-tuned, and stagger tuned amplifiers. So, the concept that we are going to discuss today is the “Stagger Tuned Amplifier”. Let us know clearly about this amplifier derivation, definition, circuit, uses, and applications.

## What is Stagger Tuned Amplifier?

Stagger tuned amplifiers are the one that is implemented to augment the complete frequency response of the tuned amplifiers. To deliver maximum flatness range all across the center frequency, these are developed. In the scenario of a double-tuned amplifier, it provides a bandwidth range of 3dB where this has deep sides and top as complete flat, but here the alignment is complicated. In order to stay back from this complication, two individual tuned amplifiers that have corresponding bandwidths with the resonant frequencies of these are altered.

Here, the bandwidth separation is equivalent to individual phase bandwidth. As because there happens to stagger for the two resonant frequencies, these are termed as staggered tuned amplifiers. The operation of these circuits can be represented using a rational function and so these are implemented to derive the crucial filter responses like Chebyshev and even Butterworth filters. As because of amplifier buffering in between each phase, the circuit poles are so streamlined to accomplish necessary response levels.

### Characteristics

· Stagger tuning procedure holds multiple benefits than that of others such as it places entire tuning elements in one combined filter. This scheme seems to be completely variant from coupled resonators and ladder networks.

· Tuning of the circuit can be achieved easily. All the components placed in the circuit might not be ideal for the other.

· As each LC section has a direct operation with a resistor, this lessens the Q factor and so any kind of losses happening in L and C elements will be eliminated by the resistor. Cascaded designs generally need a high level of Q factor resonators. In addition, Stagger tuned schemes will be included with resonator devices that have nearby values. So, the extendibility of the component values in this amplifier is minimum than compared with combined circuits.

So, stagger tuned amplifiers enhances the bandwidth range of the multiple stage amplifier at the expense of the whole gain factor. Moreover, the selectivity and the deepness level of the skirts are increased in this tuning operation. Stagger tuned amplifier circuit can be shown as below:

### Working

From the frequency response diagram of the stagger tuned amplifier, it can be known that the staggering of the circuit decreases the amplification ratio of the center frequency to almost 0.5 which is of the highest amplification range of each stage. And at the point of middle frequency, each individual stage has an amplification of 0.707 in comparison to the peak amplification of each stage. So, the voltage amplification range of every individual phase of the staggered amplifier is 0.707 times as maximum when the similar two phases are utilized without the use of a staggering purpose.

Also, the half-power bandwidth of the cascaded amplifiers is sqrt(2) times as maximum as that of half-power bandwidth of each phase of the amplifier. So, in the stagger tuned amplifier the equivalent gain B.W is given as 0.707 × sqrt(2) which is 1.00 times than that of each phase of the single tuned amplifier.

This scenario of staggered tuning can be extended for multiple stages. For example, in the situation of three-phase staggering, the initial one has a tuning frequency minimal to that of middle frequency. And the third one has a tuning frequency more than that of the middle frequency. And the exact middle one is termed as the precise center frequency. This is the fundamental principle behind the** stagger tuned amplifier working**.

### Derivation/Analysis

The **stagger tuned amplifier derivation** can be derived as follows using the assistance of a single tuned amplifier.

The effective gain of the single tuned amplifier is

Av/(Resonance in Av) = 1/(1+2jQ_{eff}_{̫}δ)

It can be written as 1/(1+jX) where ‘X’ corresponds to 2Q_{eff}_{̫}δ

As stagger tuned amplifiers are the circuits where the resonant frequencies of two separate single tuned amplifiers are cascaded, the frequencies of two stages can be considered as

Resonant frequency Rf1 = Rf + δ

And Resonant frequency Rf2 = Rf – δ

With these resonant frequencies of two stages, the selectivity can be represented as

[Av/(Resonance in Av)]1 = 1/(1+j(X+1)) and then

[Av/(Resonance in Av)]2 = 1/(1+j(X-1))

So, the complete gain of the stagger tuned amplifier is the product of individual frequencies and it is

[Av/(Resonance in Av)]cascaded = [Av/(Resonance in Av)]1×[Av/(Resonance in Av)]2

= 1/(1+j(X+1)) × 1/(1+j(X-1))

= 1/(2+2jX-X^{2})

= 1/[(2-X^{2})+2jX)]

So, [Av/(Resonance in Av)]cascaded = 1/[sqrt((2-X^{2})+(2X)^{2}))]

This gives 1/[sqrt(4-4X^{2}+X^{4}+4X^{2})] = 1/[sqrt(4+X^{4})]

By inserting the value of X in the above equation, we get

[Av/(Resonance in Av)]cascaded = 1/[sqrt(4+(2Q_{eff}δ)^{4})]

= 1/[sqrt(4+16Q_{eff}^{4}δ^{4})]

Finally, the overall gain is

**1/2[sqrt(1+4Q _{eff}^{4}δ^{4})].**

### Advantages

There are various benefits of using stagger tuned amplifiers

- They have maximum flat and wideband features
- Increased bandwidth can be achieved through this stagger tuned amplifier
- In this cascaded kind of amplifier, there exists minimal variation in the resonance. So, more stability can be achieved through the operation.
- When compared with that of a single tuned amplifier, this staggered tuning has a faster bandpass.
- Also, the configuration of the circuit is so streamlined in comparison with a single tuned amplifier.

### Stagger Tuned Amplifier Applications

Mostly, stagger tuned amplifiers are utilized in wideband applications. In the past, these circuits are used in TV receiver IF amplifiers, and currently, in the place of those SAW filters are used. Even this kind of staggered tuning has applications in very large integrated circuits for the purpose of radio applications like wireless local area networks.

The minimal extendibility of component standards allows these circuits to be seamlessly used integrated circuits than compared with that of customary ladder circuits. Used in Y-amplifiers those are working with oscilloscopes.

So, this is all about the concept of a staggered tuned amplifier. With all the wide range of applications and benefits, these amplifiers are used in various industries and domains. Also, the other concept that has to be known is the design of staggered tuned amplifiers and their importance?