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Using an fT-Doubler Amplifier for a High Gain-Bandwidth Product

Key Takeaways

  • Transistors used in an amplifier come with a unity gain cut-off frequency, designated as fT

  • An fT-doubler amplifier doubles the fT characteristics of an amplifier and provides a high gain-bandwidth product. 

  • The input current supplied to a differential amplifier becomes twice the output current when there is an fT doubler stage.

Close up of amplifier

 High bandwidth and high gain are difficult to achieve in conventional amplifiers

High bandwidth is an essential requirement of high-frequency transistor amplifiers—achieving high bandwidth in high-frequency applications without compromising amplifier gain is required. However, this need can prove problematic.  

The gain of a transistor amplifier is dependent on the input signal’s frequency—the gain is highest when the input frequency is lowest. As the input frequency increases, the amplifier gain drastically decreases until it reaches unity gain cut-off frequency, which is designated as fT. Transistors, or any bipolar device, employed in the amplifier come with fT, which is the frequency at which the gain of the amplifier is unity. At this frequency, the amplifier is not capable of providing any gain. This is one limitation hampering the improvement of bandwidth and gain in amplifiers. 

There are several solutions for mitigating this problem in amplifiers, including using emitter-follower buffers, resistive feedback, peaking with LC networks,  or fT-doubler cells. The fT-doubler amplifier, also known as a current doubler, is one solution, as it doubles the fT characteristics of the amplifier and provides a high gain-bandwidth product. 

The  fT-doubler Amplifier

fT doubler differential amplifier

The fT doubler amplifier improves fT characteristics

The fT is the index that represents the ability of the amplifier to offer a combination of current gain and bandwidth. There is always a tradeoff between bandwidth and gain. The fT- doubler amplifier provides more room for making this tradeoff by increasing the unity gain cut-off frequency.

The figure above shows the fT-doubler differential amplifier with four bipolar transistors: Q1, Q2, Q3, and Q4. The base terminals of Q3 and Q4 are connected to a common-mode voltage. Differential input voltages are given at terminals In1 and In2. 

The fT-doubling is achieved by doubling the current gain when compared to conventional differential amplifiers. The input current supplied to a differential amplifier becomes twice the output current when there is an fT -doubler stage. It doubles the current, which, in turn, doubles the unity gain cut-off frequency. 

The differential amplifier with and without an fT-doubler cell has the same break frequency, however, the fT-doubler amplifier is twice that of the simple differential amplifier.  The figure below shows the current gain versus frequency plot of the fT-doubler amplifier and the differential amplifier.

Current gain versus frequency plot

The  fT -doubler amplifier fT is greater than that of the differential amplifier 

The Small-Signal Model of  the fT-Doubler Amplifier

The high-frequency behavior of the fT-doubler differential circuit can be studied and analyzed using the small-signal model. As the circuit of the fT-doubler amplifier is symmetrical, one half of the circuit needs to be analyzed for a complete circuit behavioral study. A hybrid, pi-model-based small-signal circuit of the fT-doubler amplifier is derived for circuit behavioral studies. The figure below shows the small-signal model of the fT-doubler amplifier.

 fT doubler differential amplifier small-signal model

The  fT - doubler amplifier small-signal model is useful in frequency analysis 

By combining the voltage-dependent current sources and lumping together the impedances, the small-signal model can be further reduced to the equivalent circuit (a), as given in the figure below. The Miller transformation simplifies the equivalent circuit, and we obtain the hybrid-pi topology of a bipolar transistor amplifier with a doubled current gain. 

fT -doubler differential amplifier equivalent and hybrid pi topology circuit

The Miller transformation is used to simplify the equivalent circuit to hybrid-pi topology

The frequency range of amplifiers in RF and microwave applications is currently hitting the upper limit. The need for high performance, high gain amplifiers have led to the incorporation of fT-doubler amplifiers in RF circuits. These amplifiers emphasize gain improvement and maintain a good gain-bandwidth product. 

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