Transistor amplifier designers rely on numbers to match active devices to surrounding circuitry and to each other. They may select a transistor from a catalog, but the circuit designer has no influence over the transistor's parameters. These are set by the device's geometry, the quality of the manufacturing process, and semiconductor physics. As a result, the circuit designer must be guided by a device's measured scattering parameters (S-parameters) to determine the circuit-element values needed to surround an active device or devices in an amplifier design. This first installment of an eight-part design series will explore S-parameters; the series itself will transform any reader into a full-fledged amplifier designer.

To the circuit designer the transistor is a two-port network described by a table of S-parameters that have been measured over the frequency domain for which it has gain. After the bias and heat sinking needs of the transistor have been satisfied, the RF design proceeds using these S-parameters. At this point it is of no consequence whether the device is a bipolar transistor, a field-effect transistor (FET), or any other device whose S-parameters indicate the prospect of gain.

S-parameters are based upon the concept of incident (a_i) and exiting (b_i) waves. Customarily the b_i waves are called reflected waves, but "exiting" is a better term since portions of the bi waves actually may result from energy that passes through rather than is reflected from the network. By using a and b waves, a linear network can be characterized by a set of simultaneous equations describing the exiting waves from each port in terms of the incident waves at all of the ports. The constants that characterize the network under these conditions are called S parameters.

For example, for a two-port network, the b wave leaving Port 1 (b₁) is the phasor sum of a wave reflected from the input port (S₁₁a₁) plus a wave that passed through the two-port from Port 2 (S₁₂a₂). That is,

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and

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where:

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and the voltage at port 1, for example, is the sum of an incident voltage and a reflected voltage (V₁ = V_1I +V_1R). Similarly, the current at port 1 is the sum of an incident current and a reflected current (I₁ = I_1I +I_1R). The normalized incident (a_i) and reflected (b_i) waves can be measured with the aid of directional couplers with matched source and loads presented to the two-port terminals. This is equivalent to the measurement provided by a network analyzer. This measurement simplicity underlies the advantage of the S parameters, but it introduces a complication. Whereas the alternate Z, Y, and ABCD parameters depend only upon the network being measured, the S-parameter values depend both upon the network and the characteristic impedances of the source and load used to measure it. More about the consequences of this condition will be presented later in this article series.

When the source and load impedances are the same as those used to determine the S-parameters, the magnitude of S₂₁ is the ratio of the outgoing wave, b₂, to the incoming wave, a₁. Hence, it is equivalent to the voltage or current gain of the amplifier. Similarly, the magnitude of the square of S₂₁ is equal to the power gain.

As an example, suppose we wish to design an amplifier to operate at 1 GHz with 50-Ù source and load impedances. On reviewing tables of S-parameters provided in a catalog or in an electronic file within a circuit simulator, suppose that the Motorola 2N6679A bipolar transistor is selected for the amplifier design. The table shows its S-parameters in standard format.

The magnitude of S₂₁ can be seen as 6.6 at 1 GHz. The basic gain, without tuning, in a 50-Ù system is:

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At this point, if this is considered satisfactory gain, it is simply a matter of designing a bias circuit.² For bias, a 20-V source should be used, since the S-parameter file indicates the performance was obtained with a 15-V bias between collector and emitter. From the transistor data, it can be seen that the performance was obtained with V_CE = 15 V and I_C = 25 mA. The DC current gain, â = I_C/I_B, is not listed in the S-parameter file, but on contacting the manufacturer, suppose that at room temperature â = 40. Based on this information, the biasing network of Fig. 2 was developed.

The resistor values are calculated as follows. A base current of 0.63 mA is required (25 mA/40). However, a shunt path to carry about five times this value, say 3 mA, is desirable so that when the 15-V level falls, the base current will fall nearly proportionately. Since the transistor is a silicon NPN, the base-emitter junction behaves as a silicon diode. Hence, it will have a voltage drop at turn-on of about 0.75 V. The emitter-base shunting resistor can be calculated as:

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Practically speaking, the closest values of standard resistors may be used. This bias circuit tends to self-compensate with temperature. As temperature increases, the base current increases for a given V_BE. However, this causes an increase in I_C, resulting in a larger voltage drop in R₁, and thereby reducing V_BE.

By themselves, resistors R₂ and R₃ are large compared to the 50-Ù RF impedance level at the input. However, their parasitic elements may cause them to place an excessive load on the RF circuit. Furthermore, it is undesirable to have RF signals present in the bias circuit, since this may cause undesired RF radiation. Therefore, circuitry to isolate the bias from the RF signals is employed (Fig. 3).

Basically, the bias isolation circuitry presents a high RF impedance from the transistor terminals to those of the bias circuitry. This can be accomplished using discrete components (Fig. 3a). For the present 1 GHz, 50-Ù amplifier example isolating elements of L=100 nH and C = 100 pF might be employed. When space permits the isolating elements can be "printed" as distributed elements along with the RF circuit. The transmission lines are one-quarter wavelength long at the amplifier's RF center frequency. For the 50-Ù amplifier example, the high-impedance lines might be made Z_H = 150Ù, and the low-impedance lines Z_L = 25-Ù.