Differential scattering parameter test method for mobile phone RF circuit design (I)

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Differential scattering parameter test method for mobile phone RF circuit design (I) [Copy link]

Regarding the design of mobile phone radio frequency (RF) circuits, this article takes the test of SAW filters as an example to discuss the following three issues: how to use a single-ended vector network analyzer to measure the scattering parameters of a differential network; the common-mode interference problem when converting a differential network to a single-ended network; and the double-conjugate matching problem of a double-ended network.

When designing the RF circuit of a mobile phone, you often encounter low-noise amplifiers, mixers, SAW filters, etc. with differential ports. Figure 1 is a TD-SCDMA mobile phone RF receiving circuit, where the MAX2392 low-noise amplifier output is single-ended, while the MAX2392 mixer input is differential. Between the low-noise amplifier and the mixer is a single-ended to differential SAW filter and a necessary matching network. When designing the matching network, you need to know the differential scattering parameters of the mixer input and the SAW scattering parameters. Usually, network analyzers are not differential. The following takes the test of SAW as an example to illustrate how to test the differential scattering parameters.

Physical three-port scattering parameters

When designing the RF circuit of the mobile phone, we chose the LH46B surface acoustic wave filter of Epcos. Epcos provided an evaluation board, as shown in Figure 2. Port 1 is a single-ended input port, and ports 2 and 3 form differential output ports. When evaluating the device, first treat it as a general three-port network. Its three-port scattering parameters can be easily measured using a general vector network analyzer. The specific process is as follows:

1. Connect port 3 to a matched load, and use a network analyzer to measure the double
-ended scattering parameters of ports 1 and 2, denoted as SA; 2. Connect port 2 to a matched load, and use a network analyzer to measure the double-ended scattering parameters of ports 1 and 3, denoted as SB;
3. Connect port 1 to a matched load, and use a network analyzer to measure the double-ended scattering parameters of ports 2 and 3, denoted as SC;
4. The physical three-port network scattering parameter ST is shown in equation (1):

Generally speaking, differential ports are not ideal. By studying the physical three-port network scattering parameter ST obtained above, we can find that:

Ideally, when a point-frequency excitation signal is added to port 1, equal signals with a phase difference of 180 degrees should be obtained at port 2 and port 3, that is, a differential signal is obtained at port 2 and port 3. In fact, there are signals with equal magnitude and phase at port 2 and port 3, that is, common-mode signals. If the differential-mode signal is regarded as a port, the common-mode signal is regarded as a port, and the original port 1 is added, a new three-port network is formed, which is called a modal three-port network.

Mode three-port network scattering parameters

The question now is how to derive the scattering parameters of the modal three-port network from the scattering parameters of the physical three-port network. SAW devices are passive networks and do not contain anisotropic dielectric materials. Their scattering parameters must be reciprocal, which means that the physical three-port network has only 6 independent parameters. The differential and common-mode signals are just linear combinations of the signals at port 2 and port 3, so the scattering parameters of the modal 3-port network must also be reciprocal, that is, there are only 6 independent parameters (E3). Observing Figure 3, we can see that port 1 has not changed in the two scattering parameter signal flow diagrams, so:

SM22 is a parameter that reflects the ability of port 1 to stimulate differential mode signals. According to the definition of differential mode signals, it should be the difference between ST12 and ST13. Considering that the differential mode port is equivalent to connecting port 2 and port 3 in series, its characteristic impedance at this time is twice the original. Assuming that the phase of the port 2 signal is the differential mode signal phase, we can get

SM33 is a parameter that reflects the ability of port 1 to stimulate a common-mode signal. According to the definition of a common-mode signal, it should be half the sum of ST12 and ST13. Considering that the common-mode port is equivalent to connecting port 2 and port 3 in parallel, its characteristic impedance is half of the original impedance at this time. Thus, we can obtain:

SM22 and SM32 are quantities that reflect the ability of ports 2 and 3 to generate differential-mode and common-mode components in the reflected wave when excited by equal-amplitude anti-phase signals. Connect port 1 of the physical three-port network to a matched load and add an excitation signal to port 2:

Add excitation signal to port 3:

The combination of these two excitation signals is equivalent to adding an excitation signal to the differential mode port:

Now calculate the differential mode and common mode signal components in the reflected waves of port 2 and port 3 respectively. Their values should be equal to SM22 and SM32 respectively, and the values are shown in equations (4) and (5) respectively.

SM33 is a quantity that reflects the ability of ports 2 and 3 to generate common-mode components in the reflected wave when excited by equal-amplitude and in-phase signals. Connect port 1 of the physical three-port network to a matched load, and add excitation signals to ports 2 and 3 at the same time:

The combination of these two excitation signals is equivalent to adding an excitation signal to the common mode port:

Now let's calculate the common mode signal component in the reflected waves from port 2 and port 3, which should be equal to SM33 in value.

Its value is shown in equation (6):

Combining equations (2) to (6), we can get the complete modal three-port network scattering parameters, which are then sorted into equation (7):

It should be noted that the scattering parameters of each port obtained here are not normalized using a unified characteristic impedance. Assuming that the characteristic impedance of port 1 is Zo, then port 2 (differential mode signal port) is 2 Zo, and port 3 (common mode signal port) is Zo/2.

Common Mode Rejection Ratio

MAX2392 is a zero-IF RF receiver. To solve the problem of local oscillator signal leakage, MAXIM uses a differential mixer. As shown in Figure 1, when the common-mode local oscillator signal leaks out of the mixer input, the SAW will suppress it (the influence of the matching network is avoided here). The common-mode rejection ratio can be defined as follows:

The common mode rejection ratio reflects the size of the local oscillator signal leaking to the antenna port. The larger the common mode rejection ratio, the better. Studying the scattering parameter signal flow graph shown in Figure 3, we find that there is another form of common mode to differential mode conversion:

The quality of the common mode rejection ratio is related to the DC offset. The local oscillator signal is coupled to the differential port of LH46B through space radiation and other means. It should be a common mode signal. The differential mode signal generated by the common mode signal after being reflected by LH46B will be directly added to the mixer input, thereby generating DC by self-mixing with the local oscillator. The larger the common mode rejection ratio, the better.